I'm a vegetarian... I see the point here, to avoid animal products. If we're going THERE, then let's go there.
Plant products are directly edible (plump helmets, strawberries), brewable (pig tails, sweet pods), wearable (pig tails, dimple cup), or make an ingredient for cooking (sweet pods, cave wheat).
When you remove these, then you remove the most immediately available food source, being raw plants. You also remove half of your available booze production, your entire civilian clothing options, and many cooking ingredients.
What replacements are there? For food, there's easily fish and cattle, and if you mod then you can eat goblins and elves. For booze, you're reailly in trouble, because mead is the only other option. If you trade for booze, it's still plant booze. The easiest way to maintain drinking stock for dwarves would either be modding, or restricted sobriety. For modding, you can add multiples of bees. Copy the honeybee entry in the raws, then simply rename the entry so you don't have duplicate raws. DF has a hardcoded 40-50 limit per creature species. After reaching this amount, they no longer breed, and beekeepers refuse to handle the bees. If there's two species of bees, then you get two full populations.
For forced sobriety, use burrows. Dwarves will only leave a burrow if their life depends on it - to run from an enemy, to eat, and to drink. If placed in a burrow that does not include the booze stockpile, they will only leave it when they're about to die of dehydration. Thus, they'll drink MUCH less often, be in much poorer moods, and be slower to do anything.
Wearables are your next biggest hurdle. You can make leather armor, but not leather clothing, so your civilians will have to be armored, or be depressed. Being armored isn't a bad idea, mind you, but you'd have to handle all the different squads...
Obviously the cooking part isn't a big deal.
Either way, you're looking at depressed, slow dwarves stacked on pure meat and leather. Invest in mist generators.