Ooooo, you want to weld the pieces back together when you're done?
Metallurgically, yes, you can oil quench them. In fact, that will result in a terrific microstructure (best toughness you will get from those grades, although "best" in that family is relative...) since in quenching, faster is better. However, their high alloy content will make them very susceptible to thermal shock from the drastic temperature change, and you may find that they crack. You could end up with a great microstructure - in both pieces of the blade! Can be done, but usually requires a pretty "safe" geometry. Long thin pieces might present a risk of such uneven cooling that they will warp and/or crack. Simple geometries & smooth unnotched surfaces & regular simple strong shapes are safer, but all have some risk.
Theoretically, you could avoid the cracking risk (but probably not the warping risk) if you could just quick-quench them into oil until they lose their color (maybe 1000/1100F), then pull them out & let them cool in air, but you are taking the risk of trying to control the temp by hand & by eye. At least they would be a little easier to handle then.
If you still want to quench this way, then yes you could leave them in the foil while you dipped them, but you better ask someone who has done it about any problems with the foil then sticking to the steel.
