The brand name of slash proof bags is Pac Safe. There are several different models to choose from, some of them are rather flat, some are more like a purse, they even have backpack models. I work a second part time job in a luggage store and we sell plenty of them.
They are nice and sturdy, but I find the shoulder strap to be a bit bothersome, since it has wire through it. Instead I use a cross-body bag made by Baggalinni. Lots of interior pockets that zip closed, a wide strap that even though it could be slashed, it would take quite a bit of effort. If you keep in cross body in front of you with your hand on the bag in a crowd, I highly doubt anyone could get into it.
Just as there is no one purse that suits all people, there is no one travel bag that is perfect for all. We all have different needs. I like one large enough to hold a small water bottle, small enough my travel companions cannot turn me into their carry-all.
When we travel, we place our cash in several areas, front deep pockets, purse, under clothing belts. Never in a back pocket, never in an outside zipper pocket. If a thief got into my outside purse pocket, they would disappointingly get a hand full of tissues.