According to a Shaw article, it is possible to change one's IP address.
If your cable-modem is in "router" mode, the MAC address of the cable-modem is sent to Shaw's DHCP-server, and an IP-address is returned.
If you reconfigure the cable-modem into "bridged" mode, the MAC address of your computer (or your own wired/WiFi router) is sent to Shaw's DHCP-server, and a different IP-address will be returned.
Of course, setting the cable-modem to "bridged" mode may disable some of its "router" features.