Can coax cables be replaced with a wireless solution?
I only know of two solutions to this problem, and they may or may not work for you depending on a few details

Run Wire

If you have carpet, there is normally a small gap between the wall and the trim and the tack strip where you can just fit a coax cable or ethernet cable.  This is the trick I always used in apartments since modification to the walls was frowned on.  I've even run coax under the carpet across the room.  If you run it under the pad, you can still feel a lump when you step right on it, but it's largely invisible.

If you don't have carpet, a good solution is to get white coax and run it along the baseboard with some tacks or staples.  You can even run it around doorways.  Of course this isn't super-attractive, but it works and is easy to DIY and to un-DIY.

Running wires through the walls, attic, or crawlspace is the best way to handle this, but it sounds like you can't do that.

Send wireless video

There isn't a way to send the entire coax signal wirelessly across the room, but there are devices to send a video signal across the room to the TV.  Reading between the lines, that means that your cable box that actually hooks up to the coax will still need to hook up to the coax and have a home on that side of the room.

The wireless devices will take video from the component or HDMI output of the tuner and send it to the TV.  Some will even have a solution to handle the signal from the remote control so you can still point it at the TV instead of the other side of the room.  That means the cable box can be totally hidden, but it still has to live next to the coax cable.