The dictionary says this usage of cote is obsolete. Unlike its usage as a shed for animals. Funny, because Shakespeare uses both. Here, it is to skirt, to pass along side of. In As You Like It, the sheep cote is on sale. One is now obsolete, officially. The other, likely in use in places that have need for animal shelters, and therefore to the rest of us, it’s as good as obsolete. I like this usage of Cote, though, this skirting idea.
Before I looked it up, I thought cote might relate to coat and that Rosencrantz and Guildenstern were tagging along on the coattails of the players for a second. Instead, it’s another garment, a skirt. Relating to the French both of a skirt and also Cote d’azur. As in the coast. Which I suppose skirts the sea. Or the land. Depending on your point of view.
Thinking of these guys forming a little coast around the players somehow gives the image of passing a great deal more poetry. It makes what could be simple skirting an image I’d like to see in a painting: Rosencrantz and Guildenstern cote the Players.