At least in France, "Wear a mask" would be understood as "wear an FFP2, surgical-level" mask. The kind of masks:
* that we are in very short supply of at the moment (for various and sad reasons)
* that we have to save for doctors
* that everybody would try to buy on black markets if you asked them to use
* that we unfortunately told people not to try and buy (precisely because we need to save them for doctors because they are in short supply, etc...)
So if a campaign started today saying "wear a mask", with the intention of saying "cover your mouth with a piece of fabric that you made yourself if you're not sick", I suspect it would be counter-productive.
We need another word.