The vanilla train rush or the death wish train rush?

Vanilla.

Are any dyes/flairs locked behind the Death Wish one?

No, I don't think so. If you're not familiar with the death wish train rush, its called "10 Seconds Until Self Destruct." The title is quite literal because you have 10 seconds to get to the end of the train. Obviously this isn't possible so there's the time extenders (Clocks). So yea

Yeah

I'll prob be able to do Train Rush once I get the TIme Stop Hat, the main problem is I'm just dying normally.

Ah k, you could just do all of chapter 3, then go to chapter 4 and then go to all of the time rifts prob if you want to not do train rush until you get that hat.