If you are very worried about the 5V converter noise than you would choose a transformer with a separate winding for that ...
But , I use a linear regulator for the 5V rail + a dropping resistor and the power dissipation is not that big , it is doable . So , you are not bound to use a switching regulator .
That's a neat way to shed some of the heat dissipation burden off the regulator. Ideally you need to determine the maximum, worst case current loading on the regulator so you calculate the exact resistance value required to still leave a safety margin over and above the regulator's dropout voltage.
Unless you're trying to design for a "Universal Mains voltage PSU" with a 240v 50Hz stepdown transformer that will still provide sufficient secondary voltage(s) at 110 volt input without manually switching a split primary between series and parallel, you might want to test at the lower mains voltage limit (216vac) and check the 100Hz ripple to ensure you still have a small (half volt or so) margin over and above the regulator drop out voltage. You can then calculate the resistance required, picking the nearest preferred value that's just less than this and select a resistor with a wattage rating to suit.
Obviously, you can just make an educated guess, erring on the low side to be safe or, alternatively, just use a dc-dc switching converter to provide a fixed voltage to the regulator some 2.5 to 3 volts higher than its output voltage. If this trick is good enough for high grade commercial test gear, it should be good enough for these cheap signal generators.
Having said all that, I don't think there's really any need to eschew the use of a switching regulator on the 5v supply since the only components which make direct use of this PSU voltage are the relays. From what I can see in the reverse engineered circuit diagram for the main board, the rest of the digital supply voltages all come from the three LDO regulators supplying 3.3, 2.5 and 1.2 volts. All the critical analogue supply voltages come from the +/-12v rails which only directly drive the high level THS 3xxx opamps, another 3.3v LDO regulator feeding the analogue Vdd pins of the DACs and the +/-5v LDO regulators feeding the OPA686Ns.
If you're going to use a dc-dc converter for the 5v supply and ground return noise is a concern, you might want to rejig that 6 pin ribbon cable connector to route the 12v analogue supply grounds to the main board end of the connector independently of the 5v ground return (put the join as close to the main board connector as practicable).
This ideal can only be fully realised when all three rails are fed from three separate transformer secondaries, each with their own independent bridge rectifiers and smoothing caps. If the +12v and +5v regulators are fed from a common rectified and smoothed supply, the best you can do here to is keep the common ground wire as short and as heavy gauge as possible.
There was very good reason for doubling up on those ground wires in that overly long ribbon cable which Feeltech undid when they swiped one as a convenient way to provide a hard earthing connection to the C14's PE tag in the 6800 and 6900 models.
If you're going to go to as much trouble as building an analogue PSU to replace the smpsu board used in these signal generators, then you might as well do the best job possible or not at all imo. This means specifiying a high quality mains transformer with a 16VA minimum rating with a couple of 18v ac 300mA minimum rated secondaries and a single 8v 500mA secondary.
If you're contemplating an OCXO upgrade you'll also need to make allowance for the additional 100 to 300mA at 12v loading typical of a warmed up OXCO which might best be served by a separate analogue PSU which will allow you switch the generator off completely but allow the directly connected OCXO supply to carry on drawing power whilst it remains plugged into a wall outlet.
It will be difficult enough to find a mains transformer with all the required secondary windings let alone one with two 18v secondaries and a centre tapped 16v secondary that can be used to power 5 and 12 volt analogue regulators. Alternatively, you could choose a higher VA rated transformer with 500 or 600mA rated 18v windings and just hang another 12v regulator off the rectified and smoothed +20v output to power the OCXO[1]
Using the front panel on/off button to put these generators into standby only saves a couple of watts at most, leaving it to consume some 5 to 6 watts in this state so there's good reason to keep that OCXO module powered up independently of the signal generator if possible since it's not only the matter of the three minutes or so warm up delay but also that of "retrace" that's at issue here. Of course, if you're going to add a socket for an external 10MHz reference, the issues of warm up and retrace pretty much go away.
[1] If, when you've managed to succeed in finding a suitable transformer from which to power everything, the thought of having an additional 5 or 6 watts going to waste in Feeltech's version of 'Standby' when the OCXO can keep itself nicely warmed up and on frequency without this 'help' is any cause for concern, you can always fit powerFET switches into the DC rails feeding the regulators and either repurpose the mains switch to control them or add another separate 'standby' switch to turn everything except the OCXO off (assuming the several hours long 60ppt 'warm up drift' after an overnight shutdown escapes your OCD attention - if it doesn't, I suspect you might prefer to forego such standby economy in your quest to achieve the best possible frequency stability out your OCXO investment
).
TBH, the only reason I have such a facility at all is simply because I hadn't upgraded the psu to one capable of handling the extra load from my OXCO modification so had no choice but to add a small half amp rated 12v smpsu board which gave me the opportunity to wire it directly to the mains connections on the C6 mains socket, bypassing the on/off switch.
JBG