Simple, compact 9V DC to 400V DC step up
Could be a duplicate to this: geiger tube dc power supply.

The supply listed there works well, I can attest to it (and the guy has sold hundreds of working Geiger Counters, using SBM-20 or SBT-5 tubes).

Of course as you want to make it compact, you should redesign the PCB to use small SMT components as opposed to the TH ones used in the kit.