Frankly, unless you need to kill it, any caliber (even 22) will probably do, as the noise alone will likely drive it off...they are not normally very confrontational, preferring instead to attack from behind, hence the "look big" advice.
While I think a 22 is a waste of money and would elect to carry something more substantial if I'm going to pack, you may choose to give some serious thought to a hammerless pistol so as not to get the hammer hung up in your clothes or fanny pack. Remember the concealed weapons permit if you are going to pack and be familiar where you can and where you can't.
Watch, now you'll be prepared and never see another cougar for the rest of your fishing years....