I was worried about what to do with a small bag when I visited Barcelona to skate. I ended up keeping my phone and card/cash in my pocket and then just set my bag (containing water, extra shirt, tool, wax, etc.) down and tried to keep an eye on it. I figured that if it got snatched it wouldn't have anything I couldn't afford to lose.
And it was 100% fine. MACBA (I was there earlier in the day when it wasn't super crowded) has dozen of skaters setting their bags against the museum building so it wasn't a thing at all. At some of the more cutty spots where I was skating alone I just keep an eye on sketchy-looking folks.
Honestly, other than the caveat that every city can have rough areas, Europe is very safe when compared to most American cities. There are just so many easy target clueless or drunk tourists swarming the Gaudi spots and shopping areas that all you have to do is appear to be less of a target than them and you'll be fine.