On my Blackberry I can just disable the Mobile Network and/or data services. Which phone do you have?
Another option is to remove the SIM card to guarantee the cell service is not being used.
For some, just run the phone on airplane mode if the trip is short like to get gas.
Are you aware of affordable Telus US passes for light use across the border?
Personally I got my phone unlocked and then go crazy on data with Roam Mobility. Love Google Maps and being able to research my day's itinery while on a bus without looking for wifi.
If you insist on public wifi at restaurants and hotels... consider a VPN to minimize data eavesdropping.