Joe,
Welcome! As a true straight razor aficionado and traditionalist, I really like the idea of a barber using all the "real" stuff. BUT... I have to agree (reluctantly) with the others that are cautioning you. I don't know what the board of barbers and cosmetologists, or state board of health in your area will think, but it sounds like a potential can o' worms. If you are allowed to use a real straight, I want to come to your shop next time I'm in your area for a shave!
Consider this though - from the customers viewpoint, I wonder if they really care, or notice, that you are using a fixed straight razor or a changeable blade straight. I propose that it's the total experience that they find memorable. True, there won't be the c'flop c'flop of stropping the razor (although many wouldn't miss that since they've probably never experienced it anyways) but you can still provide all of the "old tyme" amenities of a barber shop shave, or maybe you already do. Hot towels, hot lather, face massage, and selection of aftershaves and balms, etc. Give them the works at a reasonable price and I think that's all you need.
Just my $0.02
Scott