Not sure I'm reading you right but having done leather work I'd suggest it would be best to have your custom design imprint done on a custom strap made to display it. Tooled leather designs need unfinished "tooling" leather ... not any old leather will do. Other types of leather will take other methods of imprinting. I'd contact a custom leather strap maker.
For my ukuleles, I buy Levy Leathers 1.5" straps that don't have any buckles which might bang against the finish. They're two piece with slip holes to do the adjusting. I've actually applied stick on fret markers to match the ones I put on the fretboard.
9 tenor cutaway ukes, 5 acoustic bass ukes, 11 solid body bass ukes, 8 mini electric bass guitars (Total: 33)