I got someone to cut me some freight wagon lettering in vinyl "as a favour", so I don't kno w what kind of vinyl was used, but I had no difficulty applying it to planked wagon sides of models in both plastic and cardboard, using a thin blunt tool to press it into the grooves straight away. Not overcoated with anything. Still there ten or more years later. While mine were gloss vinyl, the gentle use of wire wool took the shine off.
In commercial operations, the vinyl is often applied to a surface previously sprayed with water. This allows the vinyl to be slid around until correctly aligned, and then the residual water "squeegied out" (from the centre outwards, of course). I'm sure this would be "overkill" for our sort of applications.
To the best of my knowledge, the "vinyl" used for garments is a different thing altogether, relying on heat to bind it to the (porous) fabric. I'm pretty sure that the removal of vinyl lettering from vehicles is made easier by the application of hot air . . . so the hairdryer idea might be counter-productive in our use of vinyl.
I'm currently looking for a company which can supply me with vinyl lettering (block capitals) as small as 5mm height. I found one online (before the pandemic) who gave me a good price . . . but they stopped responding to my emails (perhaps they realised how fiddly it would be for such a modest return).
All the best
David