You need more than just the turbo. This is quite comprehensive:
You'll be better with injectors off a k04 car, so an 8P S3, mk6 R, etc. You could in theory use your k03 injectors, but you won't get full power potential, and any generic k04 conversion map will be for a car with k04 injectors.
You'll definitely need a remap, as soon after the conversion as possible. Running a k04 on a k03 map isn't a great idea.
I'd imagine most generic k04 conversion maps are classed as Stage 3, so they're designed with all the usual Stage 2+ hardware in mind as well as the turbo.
If you don't / won't have all those extra hardware upgrades, and you're essentially turning your car into a Stage 1 Edition 30, you'll want a custom map from the likes of R-Tech or Unicorn.