You can be detected at any speed - also you can remain undetected at any speed.
It depends on many factors: mainly range and enemy ASW ability
Fast attack submarines are designed for... fast moving and attack
So if you have to reach operation area 20 nmi from you in 2 hours it means your average speed should be 10 kts.
Of course being undetected depends on many factors
Better would save some time reserve and some transit make at 15 kts and more dangerous waters at slower speed.
You should monitor situation and go fast where you are safe and go slower near enemy warships / submarines.
Also you should use layer for being undetected for enemy on opposite side of layer.
Here is my video from simple training mission:
It shows you can run really fast and remain undetected close to ASW forces.
Crucial is to understand "how it works" - you can use shadow zone or speed changing.
Discussion about this scenario was here:
link
As you will see, every player have own "strategy" of being undetected. But my strategy gives you more advantages (especially in MP) than pretending whole in water