Regarding size and appearance, a DSLR is a DSLR regardless of whether it has a built-in vertical grip. Part of the OP's concern is with appearance/safety. There is no such thing as an inconspicuous DSLR other than maybe, just maybe the SL1 (with a pancake).
X100s also satisfies this need as it just looks like an old rangefinder that is much smaller than any existing DSLR today.
Apologies, I didn't intend to quote you in my first post. Must have touched something I shouldn't
However, quoting this post, I very much doubt if a 6D with pancake would attract more unwanted attention than a 100D. If this was the case the best bet might be a £350 1200D and just hand it over rather than a £900 X100.
My reason for recommending a Canon DSLR is that the DSLR is still by far the most versatile camera you can buy as long as you're not wanting something you can put in your pocket - which I don't think the OP is necessarily requesting.