I've freshwater fished a couple of times in Iceland and have done a tiny bit if shore fishing there too, but I've never chartered a boat in the sea.
have a friend though who was in Reykjavik who did charter a boat and enjoyed catching a few species including some nice cod to 7/8lb.
There are definitely options available, just a matter of getting online and sussing them out.
Am aware thought that charter boats don't run all year round so its defo worth looking into things out before you go. There is at least one tackle shop in Reykjavik, and certainly one in Reykjanesbær, but they are not always open. Try contacting them.
Don't know if you are on the WSF Forum but there is a guy on there here that lives in Iceland, he is a sea fisherman. I don't know him personally but he is very helpful and obliging. His name is Russell and his username is 'sheep'. Send him a PM if you wish, he might be able to advise.
Nor do I know about the prices of a charter boat but I do know that everything is at least double the price there..
Do it. And give us a report on your return..