Running router out of its case
About the only thing I would consider "dangerous" in a router would be the wall power.  If your router is powered from a wall wart, as many of them are, then there is little that can hurt you inside the case.

I doubt the case was ever any kind of shield.  At best it was a mechanical barrier to prevent dirt from getting in and things falling onto the circuitry that could cause shorts or whatever.

Keep in mind that the router will produce a relatively strong radio field in the immediate vicinity of its antenna.  Too much metal nearby the antenna can reflect and refract the radio waves, and de-tune the antenna.  This effectively means the range will be reduced, but this probably won't matter if the robot is not operating at the fringes of the access point's range.

The radio field can also interfere with other nearby eletronics.  Try to keep the antenna above and away from other electronic things.