No, I rinse and wipe. It's a shave so close you think that you took off the epidermis. Back in my drinking days .... when the hand wasn't quite still, I often opted to a safety razor. But, those times were far and few between. When you first get into it, it's wise to keep a styptic pencil or alum block handy. However, after a few shaves, you'll get into it like a pro. Best to have a pair, so that you can alternate .. and have a sharp one before you have time to hone and strop. Seriously, the difference in the shave ... closeness and comfort .... there is no comparison. A good pair of high carbon steel razors will last your lifetime and can be handed down for generations.
On the subject of air travel ... Now that checking luggage is an added fee and you're limited to carry-on, best not to take a two hundred dollar razor along. Stick with the 10,000 blade safety razors when air transport is required.