Thanks. I figured it was a sound approach but never having done it, and having no real background in this stuff, I wasn't sure. Better to ask a stupid question than waste resources trying something that's wrong!
The "external 10v supply" is likely to be a 10v voltage regulator on a shield that'll also contain the transistors and a pin header for connecting to several of these devices, so the common ground is accounted for.
Sorry for the confusion - I'm not actually feeding a signal to a relay - just mentioned that because it seems common practice to turn a relay with a control voltage other than 5v on/off with a GPIO pin as I've described. The device I'm feeding the signal to is made to receive a PWM signal, it just wants a 10v one instead of the Arduino's 5v.