Hey there
Yes, as far as I know, a 10.5 in boots is the same as a 10.5 in shoes. Binding wise a snowboard specific hard plate binding is needed to use the boots. I know Burton makes some as well as other makers. Maybe someone else can chime in with some info. I am pretty sure most snowboard specific hard bindings are universal to boots. Not 100% sure though.
I can do them for $60 shipped and insured if you are in the lower 48 states
Thanks, Bryan