I would try this.
Remove loose grip, clean handlebars, spray hairspray on bare handlebars, refit grip, wait while hairspray sets, ride bike.
My experience with cork is floor tiles and they only stay nice when varnished, not what you want for a grip. I suspect you will be reduced to soap and water and then live with the result.
I still recommend getting some Ergon grips when the opportunity arises.