You may alreday have a solution but it may help others. I have a Scopemeter 99 and a 99B and both of them work fine with a standard stabilized 12V power supply. I tested with an bench psu and they both work fine down to something over 7V. So stable 12V should be enough for everything.
I have two original psus. They are extremely simple. Only 4 diodes for rectifying and one cap that's it. I never expected such a simple psu from Fluke. No real stabilisation. It has an idle voltage of about 21V. It's garbage!
The plug is a DIN 45323 plug that I bought from reichelt for 73 Cent:
https://www.reichelt.de/Hohlstecker/LUM-NES1-GR/3/index.html?ACTION=3&GROUPID=3258&ARTICLE=116233A psu that would fit fine 15V/0,4A:
http://www.reichelt.de/GS06E-4P1J/3/index.html?&ACTION=3&LA=446&ARTICLE=161593&artnr=GS06E-4P1J&SEARCH=Netzteil+15VI have it running with a 12V stabilized psu and no problems. There is no difference compared to the original psu.
As battery I use 4 standard Baby C cells from Ansmann (model type "maxE"). They have real 4500mAh and are very long term stable. I charge them in an external charger. The battery packs are to expensive, have much less capacity and are charged through the internal charger unit that I don't trust. Charging 4 cells in a row is not a good solution.
Another solution if you do not need the battery option would be to use the battery connections to add a "5V input" so you could drive it with a standard 5V USB psu.