Its the height of the can that matters, the diameter has to be small for a high quality factor.
Round resonators for Gunn diodes died with the Dodo for a variety of very good reasons, including the fact that an iris / hole in a thin brass or copper sheet across the waveguide makes it very easy to control the amount of local oscillator power applied to the mixer diode. Tuning a round resonator on a small scale is, well, difficult. It takes around 15 mm of WR90 to make a Gunn LO, and another 20 mm or so to couple that LO to an SMA connector.
A 10 Ghz round resonator would be roughly sewing thimble sized.
If you want an ultra cheap 10 ghz source to learn with , HB100
Motion detectors on Ebay are 5-10$, the antenna can be bypassed with miniature hardline coax. They are DRO based.
The stability is poor, but it would give you a learning tool
Sometimes it is easier to start with Harmonic mixing and multiplication as gain is cheap.
This is a Brick, it has a phase locked sapphire rod oscillator followed by a step recovery diode multiplier.
I use bricks because the frequency stability is amazing and the phase noise is low:
https://www.ebay.com/itm/225229582241?hash=item3470baafa1:g:G74AAOSwnCtjXpcTAnother way is 576 doubled to 1152 then multiplied to 10 Ghz. This is a PCRO
https://www.ebay.com/itm/224629640503?hash=item344cf84d37:g:jMsAAOSwai5hVecv576 applied to a varacter diode mounted in WR90 followed by a filter made in the same piece of WR90 would give you a few hundred microwatts of 10 Ghz that could be amplified to drive a mixer.
I bought two of those for beacons.
Gunn Diodes are fun for Doppler radar and short
Distance wideband communications. They suck as local oscillators in modern systems. Modern systems need phase locked, narrowband, low phase noise, high frequency and high power stability oscillators. Gunn diodes don't qualify for any of that.
Google W1Ghz Personal Beacon.
It is a harmonic upconverter using pipe cap filters. With a doubler between it and the PCRO you would have a nice, clean source with moderate phase noise and excellent frequency stability.
Your also looking for 10 Ghz transverter designs.
When you said you want to apply circular polarization to a mixer, that tells me you have much, much, to learn.
In that case find copies of the various older RSGB Microwave Handbooks.
Just email Macom and ask what they have in stock
Good Luck.
Steve