I struggle to imagine there not being existing cheats for this sort of thing.https://www.almarsguides.com/retro/walkthroughs/snes/games/KirbySuperStar/GameGenie/
is game genie (so a ROM edit which can be trivially patched into a ROM, says your health gets low but nothing will happen, so presumably stops death instead of caring about health)https://www.almarsguides.com/retro/walkthroughs/snes/games/KirbySuperStar/ProActionReplay/
has a few more RAM based affairs which are harder to patch in on the SNES and probably always will be this side of strong AI.
If you need a start on decoding such things https://web.archive.org/web/20191123185800/https://doc.kodewerx.org/hacking_snes.html
One usually uses a cheat search tool for this sort of thing. Emulators tend to have their own, especially for stuff as popular as the SNES, but you can also find external ones (emuhaste, cheat engine, artmoney and many others)
In an ideal case you would have a lot of health and a minimally damaging thing you can sit there and take damage, search for anything that changed, take damage, search for anything that changed...
For platformers like kirby where you tend to have maybe three health this gets more annoying as two or three chances tends not to narrow things down, especially when "has changed" rather than lowered or specific values are searched for, might not be enough. You can boost it a bit with savestates (restore one from when you had full health and search again for has changed as it will be full again hopefully, then start once more on losing health and searching, repeating as necessary), and "has not changed" searches (if you don't take damage then the health will presumably not have changed), and if you have some kind of health restore nearby (or from a cheat/level edit) then that too can be used.
If you are better at hacking there will usually be a graphical representation of health/damage taken. Anything that causes the graphical change (be it health boxes or some kind of reaction animation) will ultimately have fed from the same thing that fiddles with health and thus you can work with that. This gets into tracing and assembly hacking though which can be a bit much, especially when a tedious half hour with a cheat search will probably still do the job. However assembly type things is also where you might stop knockback from happening*, or annoying sounds related to health being low (or enemy behaviours that might change depending upon your health).
If those links at the start are not for your region then they can still be valuable -- while the location within the RAM might change the general arrangement tends not to -- if the score is 10 bytes ahead of the health or whatever in Japanese it will probably still be that in the US and the PAL and whatever sub arrangements there are. If score is then easy to find (it is score after all, big numbers going up from easy actions) then you can go sideways from there to investigate, it is certainly how 99% of "all weapons" cheats get made or rarely modified stats.
*sometimes games will use enemy damage to determine distances here, you could find the calculated damage or something that goes into the damage calculation (say give your character 999 defence in RPGs) with normal cheats.