That's the nub of the problem.
BA's FFP says no tattoos.....End of. I suspect that other companies have the same/similar policies, so there's little point in fronting up and asking the Q when it's in black and white on the application form/page.
Running the gauntlet will be/could be fraught as if you do get found out this boils down to deceit/fraud and you'll be through the door very quickly.
All IMHO
In a nutshell, you're limiting your opportunities in an already tight market - and it'll be galling to see your peers, possibly without your skills but definitely without your tattoos - getting jobs that you're well qualified for.