Splicing small to larger speaker wire- how to

I have an unusual problem the source of which may offend the sensibilities of many serious listeners. It is based on an experiment going back to my desire to use the same speaker pair for two different amplifiers. I've only found two selectors that accommodate this issue and purchased one of them, the Niles DPS-1. The issue is that the connections on this unit will handle a max of only 14AWG wire and my current cable is bi-wired 10 gauge each leg.

So, here's the question. It's a 12 foot run to one of the speakers from the amp and I would like to use my existing high quality cable but the max size from the amp selector is 14 gauge. I'm thinking that I could splice the 14 to the 10 but have no idea if the plan would be just as good to run the 14 all the way and, if I connect the two together, what would be the best method.

My system is:
Shanling S-100 CD player; CAL Sigma 2 DAC; Rogue Audio Sphinx tube hybrid amp; Martin Logan Odyssey speakers. And:

Samsung Blu Ray DVD; B&K AvR 307 receiver to the same speakers.