With sprains and wounds, I try to go for convenient means for cold and compression.
For the former, instant cold pouches are very inexpensive. You just squeeze and shake the bag and you have ice flakes.
For the latter, I've grown very fond of self adherent wraps
, usually made from polypropene or spandex. Few wraps of it on the injury creates a sort of rubbery cast with fair amount of compression and support. In case of large amount of bleeding, put some wound pads underneath. It's also ace for a quick knee or ankle support in case of a sprain. The unhealthy part is, that it should be changed often as it does not breathe, but as first aid I find it pretty foolproof. I like that it does not come off by itself, you actually have to cut it open with scissors.
On smaller nicks that you just want to keep clean and get back training, I don't bother with actual plaster bandages as they tend to come off while fencing and sweating. Instead, I use several layers of fiber tape, the skin coloured papery stuff used for securing bandages. The glue of the tape shuts the wound and holds it together like a butterfly tape, and the porous material of the tape can suck some of the seeping while letting the skin breathe. Again, it's not the best bandage in regular use, but it gets you back fighting faster and with less mucking about. Three layers of it becomes pretty tough and its not going to rip or come off by accident. And if you really need a proper plaster, a small sterile wound pad on the injury taped with liberal amounts of fiber tape is hands down better than plaster. On the other hand it will take the hair of the skin with it when you take it off...