Thanks for the picture, the leather strap really looks great on that watch!
I have a very similar strap on my 5022 - it is a lot stiffer than the one that came on my 5001 and is just means that one crocodile / aligator spent a little more time in the sun than the other. I have not bothered trying to soften it up as it now has moulded my wrist perfectly and is very comfortable. As mentioned though, if you do want to soften it up, try some leather oils / waxes as they tend to be the best.
Dont worry too much about getting it wet - we tend to forget that the strap is made from the hide of an animal that spent most of its life under water, if it was going to get damaged by getting wet then Alligators would not live up to 50 years but I would not use water as a way to try ans soften it.