Can I fit any headset to steering column / head tube as long as it is threadless and same diameter?

You have the right idea. You can do this freely as long as the new headset is the right cup size for the head tube. The crown race ID of the new headset also has to be correct for the new fork, but 1" threadless forks and headsets use the 26.4mm ID size almost universally (maybe actually universally but there's always an oddball somewhere).

1" threadless headsets are typically all the 30.2mm cup OD size, known in their day as Professional/Campagnolo/ISO and named as EC30 in SHIS. So, most of the time what that means is you can do it freely as long as the headtube is the 30mm ID that EC30 uses. The catch to be on the lookout for with what you are doing is that there are other 1" sizes that use a different size headtube bore. The most populous one of these is JIS, which is 29.8mm. If the frame is JIS (EC29 in SHIS) you can have it machined by a shop to be EC30. JIS is common enough that you need to confirm it's not JIS. There are some other 1" sizes where it can't be made to work, but they are all far less common.