Gary,

It's not a silly question. Either way is just fine. If you rinse
try and not ding the edge of the blade on the spigot ( fawcett,
tap). If you wipe pinch the blade from the spine between your
thumb and index finger. I wipe my blade instead of rinsing.
Why do I do this...... Just do.

Just make sure you get the razor good and dry though after
use.

Hope this helps a little.

Terry