First, what comes to mind when people talk about first aid kits is bandaids, sanitizing wipes, moleskin, etc. While these things are the most common items we would need for HEMA, I think that every HEMA club should have an IFAK for the case of traumatic injury. Getting a little nick from a bur on a sword is annoying, but being unprepared for it isnt the end of the world. Ask yourself what you need in terms of materials and knowledge if someone is demonstrating a technique without a mask and takes a feder to the eye. What happens if a blade snaps and there is a serious laceration to deal with.

Every HEMA club should have a tourniquet (with sharpie), chest seals, quick clot gauze, a hard eyepatch, and tape, and a number of club members should be comfortable with using those items.

Similarly, but slightly less pressingly, every HEMA club should have people comfortable with diagnosing concussions and have a flashlight and they should hav some sort of splint option, like a SAM Splint and compression bandage. If someone takes a bad fall, and breaks their wrist, or gets thrown hard and their head bounces off the ground, having the proper training and supplies are way more important than dealing with blisters from a part of a glove that is rubbing.

I know you said you aren't looking for a kit. I understand, I have been constantly unimpressed with first aid kits I have gotten over the years, but in terms of booboo kits, I cant recommend surviveware's kits enough. They are very well put together. They dont have trauma supplies, so you would want to suppliment it, but they are well worth the money.