I survived as a vegetarian pretty easily. You might find it’s not that different for vegans, as the Japanese don’t eat much dairy anyway (one of their derogatory terms for Westerners is that we smell like milk), but you’re (probably) not going to be able to check the ingredients list in anything so mcnulty gif.
There were a few vegan cafes around when I was there (loved the PETA one in Shibuya) and I don’t suppose it’s got worse since, but relying on them will limit your travel options, and the cost will stack up.