It's 1:30 am and I can't sleep, so....
Experiment to see if you can find / modify a soldering iron/ miniature soldering iron with a similar sized tip.
A lot of the cheapo soldering irons I see on a quick internet search have removable tips, so you could modify them as needed.
The biggest potential problem I see, is when the plastic melts, it will "blob" around the site which might (or might not) interfere with the precise 5/32.
I would also possibly experiment with heating a smaller diameter drill bit up itself and twisting it clockwise on insertion to engage/catch any melted "bleb" in the drill flutes to get the majority of the hole completed, then going to proper size drill bit (or tubing- like devodave mentioned) to finish. The initial drill bit (perhaps a 1/8 or smaller) would be a twist/engage/pull motion. The idea would be to at least pull the excess towards you where you could shave it off with an exacto knife. The final size 5/32 would be a small step up from the previous sizes. It might require going through several smaller sizes incrementally to get to a clean final hole.
I would experiment on things like "tic tac" plastic containers etc. first to get a feel for what works.
edit- Now that I think about it, a mini torch might be easier to heat the tip of something up, like a punch.
more edit- I can't complete a project without buying something at harbor freight. These punches would hold heat well and have various sizes to experiment with:
https://www.harborfreight.com/8-piece-punch-set-93424.html?cid=paid_google|||93424&utm_source=google&utm_medium=cpc&mkwid=s|pcrid|385337702124|pkw||pmt||pdv|c|slid||p roduct|93424|&pgrid=73846655970&ptaid=pla-310099998185&pcid=6549823817&intent=&gclid=Cj0KCQiA6IHwBRCJARIsALNjViX0_NCcaK3n12Aqkx2Z 8hX2l2KwnG4uMF2_78XAqLTDPF-6n7ggwSgaAiwIEALw_wcB