Just leave the blade in and clean the razor when you change the blade. You really think our fathers and grandfathers over thought this like many do ? No .
BigMark is absolutely correct. Per step 4 of Gillette's Super-Speed instructions just loosen, rinse, & shake out moisture. Do a thorough clean with blade change.
I take the blade out, dry the razor. clean the blade with a towel, and put a light coat of pre shave oil on the blade on both sides of the edge
I take the blade out, clean and dry the razor. rinse the blade and dry with a towel, and put it all back together for another day.
I do just what BigMark says with stainless blades. On the rare occasion I use a carbon blade, I will rinse with rubbing alcohol to help displace some of the water to try to prevent rusting.
Well, @BigMark, maybe that is why so many vintage razors are coated with crud. Some did not think, much less over think.