Thanks to all for the reply's.
Good point Blip noted. It's indeed a false assumption to use the word 'push the rudder', while reducing (smootly) pressure on the pedals close to Vr and thereafter to maintain track is what you actually do.
Sometimes I lost a bit the picture of rudder use during crosswind take-offs
. But everything is much more clear now.
Luckily the past few days were windy in the UK and Ireland, so I could practice your advises in real life...
Happy take-offs!
The Snake