Fortunately the Nikon Photomic FTn meters were pretty easy to recalibrate for silver oxides, so mine are set for those. Unfortunately it's become quite hard to find the big batteries in silver oxide now, so I had to make little metal rings to fit smaller ones.
Hearing aid batteries are usually zinc-air (which I think performs better under heavy load). If they have a pull tab, they're zinc air for sure. I've used hearing aid batteries in Konicas, which are both difficult to adjust and very intolerant of voltage variation, and found they worked pretty well with an added 2/3 stop ASA offset. They don't last very long, and it takes a day or so for the voltage to stabilize, but it then stays pretty constant for the duration. The Konicas had a nice battery check which was ASA dependent, so it was really easy on those simply to run the battery check and adjust the ASA until it was right. The result was nice and precise.
I've heard that you can stretch out the life of zinc-air batteries by not unblocking all the holes, and somewhere I read a recommendation to dab a little glue on all but one or two. I never tried it, in part because I gave away my Konicas.
Other cameras I've had worked moderately well on alkalines, seeming to be less bothered by the voltage variation, and again if you have a standard against which to measure the reading, you can adjust the ASA to correct for voltage. I've had some alkaline batteries that went fairly quickly down to 1.35 volts and then stayed there for a long time. It's hard to predict, but it can come surprisingly close. It's always good to try them, because some meters are not all that accurate anyway, and sometimes you get lucky. I had a Yashica Minister that was spot on with an alkaline.
The Pentax spotmatic, as mentioned, is not voltage dependent and will work with modern batteries if you can get the right fit.
Unfortunately, the Nikon Photomic uses a side contact for the battery, so you can't just use an O-ring on a smaller size, but on some cameras with contacts only at the ends, you can.