The bracelets aren't the issue, but the end links. The lug holes for the bracelet spring bar in the Speedy Pro are very far away from the case, so you can conceivably install the 20mm AT, PO or even RM bracelets on the Speedy but there will be a noticeable gap and considerable play since there's still room between the case and the end links.
You might be able to extract solid end links from a modern Speedy Pro bracelet and reaffix them onto one of the aforementioned bracelets, but I've never see it done successfully.
I've heard of some people using 633 end links on newer AT bracelets, but haven't seen it in person. Even then those are hollow end links, although the newer style with the additional machining are a bit more stable than the older ones.