That wouldn’t be a problem at all. Many businesses already do this (DAS design) either customer specific on their floor/suite, or the building has a full blown building wide system each tenant can jump on.
Wireless in-building can and will replace wired for most companies for general use (with wired connections directly to servers and not employee level computer work).
Really the only issue is user error from employees (initial connections). In-building antennas permeate through everything fairly well except solid walls, but they still can bounce around solid walls pretty well.
Honestly it makes the most sense for skyscrapers like NYC where tenants move and demo floors every few years. Leaving backbone fiber connections only to their Server rooms.
Honestly this would only make sense if the pistol was pointed at the user in case of capture.
If you ever shot at a threat with this you better have wanted to cosplay a clay pigeon at some point in your life.
Let’s assume cost isn’t an issue and there’s some advanced computer onboard for quick aiming… you have 30 shots (maybe)?
Your hands should not act as thrusters if the goal is to do anything except fly. They would be 100x better designing some leg mount system with a frame/protective shielding from the thrusters.
This is assuming there’s any practicality in having a person involved instead of just using a drone (which there is not at this time).