Is the cable modem wireless enabled or is it a separate wireless router? When I had a cable connection in Sydney (sorely missed by the way), the cable modem just had an Ethernet connection into which you could plug a router. I had a dedicated firewall device and my wireless router plugged into it. As long as the modem/router has an ethernet interface to connect to another wireless router, you should be OK as long as it's possible to disable wireless in the existing device.
I currently run a TP-Link wireless router and it's working well. I can get a reliable connection on my mobile phone up in the shed which is about 25 metres away. No problems with signal anywhere in the house.
EDIT: My wireless router is TL-
MR3420 which is designed to take a 3G wireless dongle. It's not currently used that way and is just plugged into my ADSL modem.