You do need fancy equipment, but not quite that fancy. The one thing you absolutely can't do it without is a nebulizer. This is a sort of modified spray bottle which converts liquid into aerosol. A regular spray bottle won't work, because the droplets it produces are too large. The nebulizer I have works by having a channel which pulls liquid up and suspends a drop of it in the path of bursts of air, which you produce by squeezing a rubber bulb. This is an expensive item because it's in short supply, but it's a simple plastic part that would be very cheap if it were made in bulk, and it doesn't seem impossible for someone to make a replacement home with hand tools and some expertise.
(A commercial fit-test kit will typically contain two nebulizers, when you only need one. The reason for this is because if you're following the formal procedure, you first use a low-concentration version of the aerosol to make sure the person has a working sense of taste, then a high-concentration version for the real test, and if you're testing a bunch of people in a row you don't want to have to clean out the nebulizer each time. For home use, you only need one.)
(The liquid you put in the nebulizer is just saccharin in water; you might as well use a bottle that's labelled as being for fit tests, but if you can't get one you can get saccharin powder at a grocery store and mix it with water yourself. Some test kits use denatonium aka Bittrex instead, supposedly because some people can't taste saccharin. A saccharin test is much more pleasant. I noticed that saccharin solution sometimes clogged the nebulizer, by leaving a crystalline residue when it dries out, and denatonium doesn't.)
The formal fit test procedure also uses a hood, which holds aerosol in place while you hold your head at various angles and read a passage aloud, in case gaps open only while you do that.
When I've administered fit tests to people, about half fail. Cheap KN95s usually fail by having big gaps around the edges, which can be fixed by taping them down with medical tape, if you really need to. Rubber interface P100s fail by not having the straps tight enough or by having incorrectly installed filters.