Nearly all coax is quite lossy at those frequencies, for a run more than a few feet / a meter. If you can get it to work at all, performance will be quite poor.
A better solution is to get the transceiver as close to the antenna as possible, then do a long cable run from that.
A similar thing is done for satellite antennas - ever heard of an LNB? They amplify and downshift the signal right at the antenna, to mitigate the losses of a cable run.
The "LNB" is just an analogy - you need to put the access point outside, then run Ethernet cable from that. Power over Ethernet would be perfect for an application like this. Look up "outdoor wireless access point".
If you absolutely cannot run a new cable, here's a wild idea - use the existing coax cable just to provide DC voltage to the access point. Set up the access point to cross-band repeat, then use another access point inside to get the data onto the rest of your network.