It looks from the photo that if you take those screws out, the wheel will come away, leaving a cast hub unit which fixes to the steering helm. You may find it easier to get the puller onto the hub than the wheel.
Good luck with it - these jobs often result in a new helm being purchased too
Loads of different steering wheels available - they all tend to have the standard 3/4" morse taper to connect to the helm unit so are pretty universal. Just choose one you're happy with. Be careful of getting something too big, as you may find it awkward in a bucket seat Searider.