You could leave it dipped in alcohol, however it must be in a sealed container, - otherwise the alcohol will evaporate fast. The alcohol prevents oxidation of the blade which should give you a smoother subsequint shave. You could leave it dipped in oil as well.
I remove the blade after each shave. Towel dry the DE razor and fold a corner of the towel over the blade and press to remove any water. Never rub a blade for 2 reasons: #1 and the most obvious, you can cut yourself easily. #2 and less obvious, most blades have a microscopic coating which makes them so smooth. Rubbing will remove the coating and you will have an un-coated blade for your second shave and it will be a little harsher then the original coated blade. SO... I just place the blade on a towel while I am drying my razor then just fold a corner of the towel over the blade and press to remove any water.
I will keep my TTO open and my 2 and 3 piece apart until the next day when I put them away and bring out another razor to use.
I shave with a different razor and brand of blade each day.
Storing your razor in alcohol or any solvent will effect the plating/coating and reduce its useful lifespan.
If you are worried about "germs". You can emerge your razor in a glass of alcohol for 10 minutes every once in a while (no more than once a week).
This is not necessary as long as you are the only person using the razor. If you share a razor you might want to give it an alcohol "bath" before each use or invest in a barber's soak jar and some Babicide or Marvicide commercial disinfectant.
If you use a commercial disinfectant do not place anything in it for longer than 10 minutes to avoid damage.
Great info, gents. Thanks. Not a germaphobe, but the theory is that alcohol eliminates the water and prevents blade oxidation. Thought it was worth exploring.