Here is just a map of parking availability in the downtown core. All of the city lots are reflected by the green numbers (as the city of Hamilton has so labelled them). In addition, I've filled in red several private pay lots that I'm aware of (however I could be mistaken). In addition, the lands surrounding the potential stadium, and Jackson Square (due to their underground parking) have also been noted by the spray effect of red.
This map excludes other potential private lots, of which many I can see being agreeable to charging for their spaces during a game, just as many currently do by Ivor Wynne. This also of course, excludes the various street meters in the core, which would no doubt be used, of which the city cites there being over 800. It also does not include the lands the city managed to acquire from the "housekeeping" land claim, which they have also claimed will be converted for additional parking. I should also note, nearly all of these listed locations are surface lots, save for #68 and 69 from mu understanding. Not parking plazas, meaning there is room to accommodate additional parking plazas.
As far as being able to walk to the stadium I have no doubt Mr. Young or the city would be happy to create/reserve/sell seasonal handicapped parking spaces the closest potential parking for the stadium for the disabled. The main reason I'm displaying this is to show the ample parking that is available in the core, and it's proximity to the suggested stadium. It also speaks volumes to how much city owned parking is available and how much potential revenue a parking "kickback" could offer the cats.