So your evidence of a leak is "the oil was a bit milky".
This is a matter of proportion.
I have changed gearbox oil, in total over hundred times, in at least twenty different engines and I've never found one that didn't show some evidence of water in the oil. It's just something that happens (The Seloc Mercruiser manual actually tells you how much water in the bottom of the drive is acceptable) and quality OB gear oil is formulated to perform with some water contamination.
Unless there is a visual or obvious sign of an oil leak I'd just give it a flush, put new oil in it and try it.
Keep checking it every time you bring it home until your confident it's ok.
It's a different kettle of fish for a boat that's left on a mooring but I think you could be getting your knickers in a twist about nothing