Can I Hook Up RX-460 to Regular PCI Slot via PCI-E Riser
No.  PCI and PCI-e are two entirely different things.  PCI is a more traditional parallel data channel, while PCI-e is a serial data channel (that can have multiple parallel "lanes").  

You cannot plug PCI-e devices into PCI sockets.

If you're desperate, you can try the mechanism specified here, no guarantees though :)

https://www.youtube.com/watch?v=5vDHACwXSxE