Based on doing what you're planning to do over 3-4 occasions in the past year: about 6-8 minutes between trains is about the fastest it can be done. Best to be in front 8 coaches if possible: there is a passageway that was put to ease the connection at the midpoint of the platform, but this has been shut for security reasons for some years. Although in general there has been no security all pax are funelled through an area beneath Platforms 3/4 where they can be inspected if the security is tightened (it's up to the Belgian authorities what security they impose on any given day). Also, the Belgian customs are there some times presumably looking for drugs, stolen goods and people moving more than EUR 50,000 between EU member states, without filling out the official forms.
The 3rd time I did this journey, the ES was about 8 mins late due to something weird near Halle and the ICE wasn't held. So I had a 2 hour wait. The non-ICE option is OK, but the shuttle from Welkenraedt to Aachen is one of the oldest EMUs on SNCB/NMBS and it really feels like a museum piece. Another time, the ES was late (I think by about 5 mins) but the ICE was held...
The overall reliability of the ICE trains is now very poor so I would always allow a contingency of c.3 hours for any onward connection from Cologne (eg. sleeper trains). It is one of the poorest ICE lines that DB operate -- the catering is totally random as well -- and a pale shadow of what it was ten years. But once you switch onto an ICE4 at Cologne or Frankfurt and zoom where you are going to Germany, everything will feel much better again.
The plan is for SNCB to provide an hourly Cologne - Brussels in a few years' time, when they have new trains, which should make things miles easier!