You can do it with a constant offset. This allows the client to see into the future while taking actions in the past. If you learn that in 100 ms you are going to be headshot you can take actions while in the past to save yourself.

Anything that is "constant" is equally trivial to detect statistically.

To hide the fact that you're always lag spiking 100ms when you see an enemy, you'd have to lag spike randomly all the time, quite a lot, and then you're asking for a kick for low ping.