Your fine. The blue lube is probably the Mercury High Performance Lube which is a synthetic blend I believe. Your going to drain out the old so there won't be enough left in it to harm anything.
And yes, There can be compatibility issues.
You could let it drain overnight, or for a few days if you wanted to.
Or, you could swap the Yamaha lube and get the Mecury high performance lube.
It's what most of us down here use, regardless of outboard brand because it holds up better than anything else. I use it in my twin Yamaha's that we run offshore in 100 to 200 mile trips on a regular basis.