Sorry but being bound to player is stupid as hell.
1)If I want it a different character, or I die I either: A)Inherit it, gay B)Lose it
2)If I swap mains or want it on many characters I have to pay many times. I guess this is fine and all, but also makes switching characters ridiculously pain in the ass for this as well. If my Melee was my previous main and I swapped to my Marksman as my new main due to the change my old main which is now mostly useless has all the money I put into it.
Also it makes no fucking sense for it to be character bound instead of item bound, besides hair.
The biggest call I'd see for cosmetics would be:
1)Recolors (dyes) - Which as you've stated and I agree with, don't make sense as 'cash shop' but as findable ingame
2)Hair changes - Which as jorb and loftar have said before and I believe you have as well should be based on time, cutting your hair, and possibly sliders. I also agree with this.
What exactly do you expect to be sold in this 'shop' then? Those would be the major contenders and they make no sense to be anything else. In fact, nothing makes sense to be cash shop in a game where everything is run by players, you get it by your own hands, which makes perfect sense and is perfectly fun. If you can think of something though, please let us know.