Sir redjastin,
If your Valveking has send and return, Just put you GT10 mono output in the return input of your Valveking.
And your GT10 would be your Master volume also it that will not color your COSM modelling. Select which output options like JC120, Small Amp, Combo Amp with gear you have. I would advice using FRFR system when using GT coz FRFR like Keyboard amp, PA system and you no need to bring along your guitar Amp
BTW are you a live player, garage band coz GT10 for me is design for FRFR system (Full Range Falt Response) like PA system. If your a live band great just direct your GT10 to you mixing console and use DI box Plus DEC in your GT10. Thats all, you'll be having all the COSM model amp at your hand
Happy New Year