I guess a 12ax7 is doable , but proper power hungry tube circuits inside a box that size ,not really ,
Hey good lookin' what you got cooking ?
I prefer my electrolytics rare ,never well done .
Somewhere in the BBC archives is a tiny matchbox sized tube preamp , runs off battery power and hearing aid valves. Might be worth a look for reference .
The DL64 and DF64 series tubes ,
http://www.r-type.org/addtext/add177.htm
For a DL64 with 15 V HT the output is 950 microwatts at 10 per cent total harmonic distortion for 0.85 V grid input and a cathode current of 184 micro-amps, probably more power in a fly beating its wings ,but thats not of any consequence if you have silicon doing the heavy lifting at the front and back end .
I second Mr Bells suggestion for making up a small switched HT board , I've found myself on the same meander in the post on battery tube mic supplies
Heres a really nicely written article by Jan Rychter ,
https://jan.rychter.com/high-voltage-power-supply-for-nixie-tube-projects