It's been a long time since you asked this question and I hate to see it get no response. I can't say I have a definite answer for you. But I can say I have looked at a large number of period photos and I've done some reading on Canadian forces websites. I haven't found any mention of wearing both sets of wings in any formation. The same goes for those who trained in the US and went on to become members of the Special Service Brigade. In both cases it would seem Canadian wings were worn. I do know the Canadian Government was very sensitive about the issue of Canadians serving as Canadians, and that they sought to maintain control even when Canadian forces personnel were attached to other nations units. This is an interesting question and intend to do more research. In the mean time please post if you find an answer.
Tim