Lock to fit around Big Apple tyres (28x2.35)
I'd guess the big apple will make it tight depending on what you lock to. 

Certainly the long shackle variants or standard shackle variants will fit around this. I have a Kryptonite New York Lock in a long shackle variant can fit around pretty much anything. 

When you get the bike, you can easily measure the width the lock needs to have along with the length of the shackle to lock around what you need to lock to. I carry one New York Lock Long Shackle and 1 Fahgettaboutit so that I can lock in tighter places (and lock both the front and rear wheels with U-locks). I'd think even if the mini isn't suitable for locking ot something, it would be good to lock a wheel to the frame (and use another U-lock to catch the other wheel and whatever you need to lock to).