Personally I would not add mayonnaise to garlic butter for a cold sauce as when you chill it either it will go very hard when the butter hardens or more probably the butter will not have mixed with the mayonnaise properly and you will end up with hard lumps of garlic butter in your mayonnaise, also it won't be very nice. Just add some garlic to some mayonnaise and some seasoning. Personally I prefer to roast the garlic gloves in their skins in the oven untill soft and then add this (without the skin) to the mayonnaise as the flavour of raw garlic can be a little harsh.