Interesting situation.
We presume you are
not, having read all the warnings here, allowing any soap to get inside your foreskin, as that is a definite source of irritation and itch.
Reading a little further back into the threads here, you would have seen it mentioned that the major concern about using the steroid creams is that they can make it easier for Candida ("Thrush") to develop in the moist area under the foreskin, so you might consider using one of the readily available (Over-the-counter - "OTC") anti-fungal treatments containing clotrimazole or miconazole (or a couple of others) under the foreskin. If that cures the itch, then you have a reasonable proof that was the trouble (in which case, just keep the anti-fungal and use it whenever you need to); if it does not, then pretty clearly that was
not the cause.
On the other hand, the hydrocortisone is in itself a useful treatment for itch and dermatitis, so if it
was helping, you could safely use it in conjunction with the anti-fungal.
And it may just be that the itch is a straightforward consequence of the stretching, although (as best I recall) this does not seem to have been mentioned before. However it may be, it most
certainly would not be any reason to restrain your activities in doing the stretching.