what wrench will protect chrome fitting?

Most (but not all) shower-heads have flat surfaces for a crescent wrench. Shower-heads do not need to be overly-torqued, so there shouldn't be any damage to the chrome.

And fwiw, I've never found a strap wrench that worked. If there aren't flats for a crescent, I look for creative alternatives. Like when installing a shower arm, I'll put the handle of channel locks into the arm and turn.

Improvise, adapt, overcome.

Tape, as suggested by SumDude and Master Roy. Use a piece of cloth around the fixture to protect it. Washcloths, towels, shop rags, all can be forced into service. Or, an old piece of rubber, from a hose or tire can be used, making what you describe.

Or, dip the tool in a rubber solution that is used for grips on rackets and other sporting equipment or tools. I used to have a can of red and a can of black that I dipped all of my tools in to make an improvised shock-proof handle cover. You may have to dip this several times, or break it into it's parts if it is a complex tool, but...

Make sure you wrap Teflon tape over the arm threads and then it shouldn't have to be tightened so tightly to prevent it leaking. I usually just use a cloth when I put a crescent wrench on a chrome fitting.

You seriously have no life FRANK seems like all you do is be on yahoo answering questions with ignorance no advice what so ever just to get points who does that, you must be a lonely person with no one who loves you since all you do is spend your time on the computer trying to bring others down then you want to report comments like the little ***** you are lucky for you this is the internet since you seem like one of those people who walks around with their head down whispering to themselves because they don't have the guts to say what they think out loud if they were face to face with you and NO this is not a threat or harassment since you seem the type to try to take this to the highest degree of "punishment" this is simply freedom of speech and publication and exposing you to everyone who reads this before you go and complain to yahoo for them to take this down lmao. Get a life this is supposed to be a safe place for people to use their freedom of speech to post questions and get answers without criticism from dumb asses like yourself.

wrap the shower head nut with elect tape , a couple of times around will work fine

idea : put duct tape on the wrench gripping part