First off, I'm talking about a vent pipe not an exaust fan.

I'm putting a bathroom in the basement of my ranch home. Since the only bathroom is on the first floor the vent pipe is not currently accessible from the basement.

The clear solution seems to be to open up the wall on the first foor and attach a pipe to the existing vent pipe than bring the new pipe into the basement.

In a perfect world I'd like to avoid this. The walls are plaster - a mess to patch, and the wall to best access the pipe is in a bedroom.

Is there any other way? Hooking into the radon or furnace exaust?? <yeah right! What is not an option is an air admittance vent as I'm using a grider pump.

Any guidance would be helpful, before I punch a huge hole in the wall.

Without a doubt you can NOT tie your vent into the furnace or radon vent. If you don't want to tear up the plaster you could go out through the foundation wall and vent up the side of the building, through the eaves and roof. It won't look much worse than a downspout.