I just had my Jeep's transmission fully rebuilt and the rear axle fully rebuilt. Cost a pretty penny, but was worth it!

So, after getting some of the major things replaced, I decided to do some cleaning and detailing to my Jeep. It's a 95 GCL. One thing I wanted to, as I've never done it before, is to degrease underneath the hood and hose it all down. But here's my dilemma:

Is it safe? If I go to the do-it-yourself car wash and use the pressure hose w/ gun provided and on the "Degrease Tires/Engine" setting, will it be safe or damage my Jeep? Also, would it really do much to remove gunk from the top of the engine and all the other components or would I need to buy something and pour it on all over prior to hosing underneath the hood?

If it is safe.. should I do it while the vehicle is running or off?

Thanks!