No idea if it did cost or not - many moons ago now
If it did , it wasn't a lot ( like £10) cause my pockets were mighty shallow in those days
DVLA was free as it was a date specific plate and not private - don't know if that has changed.
When the feds are filling out the form just tell them it's a 1991 bike and when that goes off to DVLA your plate will be that year.
To save time, and they insist - scrape the paint away from the frame numbers, They need to see that it hasn't been brazed and re-teeped.
I had just smoothrited mine

but worth it to get it plated.
BTW, even with your kwak document I think your still going to have to prove it's not stolen otherwise it would be all too easy to steal a bike and ask Kwak,Hond,Yam or Suzuki to issue paperwork for them.