Personaly I would opt for water fast. Eating a little bit of veggies would probably just ignite my hunger. I suggest you go easy on yourself and not plan loads of strenuous work during your fast. Many people report the first 48 hours as the hard ones, then they kind og fit into it, and hunger pretty much subsides.
There is a lot of marketing hype surrounding exogenous ketone supplements. But I can`t tell you if they are actually worth your money. I have tried with a litte BHB in the morning when fasting, but can`t say I felt much :)