This is an area where I have some ideas to help you find something unique and save money at the same time. That said, I really must encourage you to scroll up and consider a couple of the items mentioned in this article. It seems to me any wall-mounted bottle opener listed for about five dollars is cheap and worth the few bucks of its price tag.
In addition, here are some other ways to find the right wall-mounted bottle opener for your budget.
First, you could go to Amazon and search on wall-mounted bottle openers. Sort the results by low price to high price, and shop based upon that information. You will have many to choose from at around five dollars.
Secondly, you could shop with junk dealers. Somewhere near you, I am sure, at a store that deals in older, sometimes rusty, items, you can find a wall-mounted bottle opener with some history -- some character -- that will please you and your time-to-time party guests.
While out in the bliss of the outdoor world, seek yourself a thrift store, like Goodwill. Peruse their shelves and you may luck into an old wall-mountable bottle opener at a price in the ballpark of a dollar or two. Now, that is getting away cheap!
Finally, keep eBay in the mix as you shop for cheaper wall-mount bottle openers. That is just the sort of item for which eBay was created.