As long as he is eating and acting normally I would NOT put him down, fins CAN and DO regrow. Putting something like panty hose or netting over the filter intake (depending on what kind of filter) may help him from being stuck again. Keep him well fed, and keep his water super clean. I would use melafix and pimafix to help, but that is a subject of great controversy. I know it helps tissue regeneration and has anti fungal, viral and bacterial properties in humans and other mammals, and tho others argue fish tissue is different, I have seen it speed recovery of fin tissue vs not using it. Personally I would never give up on a fish that still has the will to live (i.e still eating and responsive)
If u ever DO need to put down a fish, clove oil is most humane, it is an anesthetic and will put them to sleep.
There are many articles about using it, best is to add it gradually mixed with water in a small container. 1/4 to half a teaspoon per gallon of water, or a few drops per cup. Some have recommended after the fish is deeply asleep adding alka seltzer to the (closed) container which will speed the end due to carbon dioxide overdose. 2 tablets per litre of water. Just using clove oil alone can take awhile more than an hour, but since the fish is asleep, u can add a bit more or wait it out.
I have heard from veterinarians and from reading scientific research, that freezing cold blooded creatures is not painless, ice crystals can start to form in their brains while they are still alive and it is speculated this is not pleasant. The AVMA does NOT recognize freezing as an acceptable form of humane euthanasia.
In warm blooded animals, hypothermia would kill u long before your brain froze. Freezing a VERY deeply anesthetized fish might, in theory, be painless.