Not providing alcohol but...

The problem you'll have is that other people will order alcoholic beverages and not get them paid for, and she'll order them and get them paid for. This may cause resentment among other guests.

I'm not sure how to sneak paying for grandma under the table but not anyone else. I'd either let grandma buy her own alcohol, or buy everyone to avoid anger or confusion.

Yeah I'm trying to see how it would work to do it "in secret" if we've announced we're not providing for alcohol. I already have to let my sister know to tell her daughters not to order any virgin cocktails because they're also not included so definitely may cause some resentment if I'm paying for scotch for granny.

This is difficult since alcohol will be readily available. Are you hoping no one will drink at all? Or just not paying for it?
As someone who drinks socially, I would probably order myself a drink unless someone actually informed me it wasn't allowed.
If you are OK with people drinking but just not planning to pay: how will you convey that message? If a bartender/waiter came to me and asked for my drink order I would probably order a glass of wine- I wouldn't know it wasn't going to be paid for.
Just make it clear to your guests what the deal is. But I don't think you should pay her tab if you aren't paying anyone elses.

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We're having a small-ish wedding of about 25 people. I think there are only two "drinkers" in the bunch besides me and FH. We aren't paying for alcohol and have made this clear to each of our guests. I think my problem is I know that my grandma is going to drink anyway. I guess I should just let her pay for her own.

I don't see any way you could do this without possibly offending your other guests. I'd pay for everyone's drinks or none at all

I think if you tell the restaurant that it's a non hosted bar, they'll know that the guests have to pay themselves.