Already been done.
Back in the 60s, a Chipmunk was re-engined with a turboprop of about 90shp (I think).
Reg was G-ATTS. It ran at pretty much constant rpm and speed was controlled by prop pitch. I remember the flight test report saying if you reduced to ground idle in flight, it was like running into a brick wall!
Take a look at
De Havilland Canada DHC-1 Turbo Chipmunk 21, G-ATTS, Hants and Sussex Aviation