Is it legal to use different wire types for pig-tails?
It's OK to mix types of wire.
There are no exceptions to the color-coding or re-identifying rules for pigtails.  For example you could not use a green wire for pigtails with the hot or a black wire for a neutral pigtail.  What's clear to you today when you do it may not be clear to the next person looking at the wires folded up in the box.
If you were to re-identify a pigtail by taping the insulation end to end, it's pretty hard to imagine anyone complaining about that, even if it's not strictly compliant.