He's still going to want support within England; Burgundy or whoever might lend him money for mercenaries, but that's not going to be enough troops. It's worth remembering that all of the successful WOTR cross-channel invasions (the Readeption of Henry VI, Edward IV strikes back, and of course Henry Tudor) were supported by significant forces raised within England. I'm just not sure there are enough unreconciled Yorkists left in positions of power post-Stoke Field.
Scotland might be able to provide an army, but the performance of Scottish armies in the Wars of the Roses was not exactly stellar.
Henry VII may not have been the most inspirational war leader, but he had perfectly competent generals like Oxford under him, and was willing to allow them to go about their business.