transistor pre with the sound of tubes

There is NO such thing as "tube" or "transistor" sound! Only a CIRCUIT has a SOUND! The big advantage a solid-state device has over a vacuum tube is that the former is free from aging effects. While the vacuum tube has a finite life-span and degrades with use, alas!

BAT VK-40 had a reputation to be warmer than their tube preamps.But I don't understand your fundamental problem to just buy a tube preamp it that's the sound you prefer. BTW I am using an Ayre K5-xemp.

"I’m not liking the idea of what people say, tubes must get warmed up first. I also am a bit worried of injecting noise."

You're reading too many audio threads. Stay with whatever you have.

NO TUBES FOR YOU!
https://www.youtube.com/watch?v=zOpfsGrNvnk

" But I don't understand your fundamental problem to just buy a tube preamp"
The fundamental advantage of SS is you can leave it on 24/7.
You can do the same with tubes if you don't mind replacing the tubes every so often.

no transistor sounds like tubes