Please. Jeans were originally strong work wear for no-nonsense types such as cowboys. Can you imagine the Marlboro Man daintily tipping a capful of expensive soap into a basin before he hand-washes his jeans? Come now. Many denim authorities actually recommend washing jeans as rarely as possible to avoid premature fading. For a new pair, some suggest the first soak should only happen after about six months, or when there is sagging around the knees or seat. Raw denim such as yours is dyed but not set with deep indigo. Colour will run easily, which would not bode well for lighter items haphazardly thrown into the machine with them. I always turn mine inside out before every wash.
Don't do it. That's the best advice you're going to receive. I was so flabbergasted by the very question, I consulted some shaving experts. They, in turn, asked not to be quoted on your Kamikaze mission. They said an aesthetician would always suggest waxing over shaving to avoid razor burn around the sensitive pubic area (ouch), and reduce hair growth over the long term. Post-removal care is vital, including exfoliation (ouch again) and cream. Really, is a little less perspiration worth all this?