I would have thought that was a question for the EndNote forums. There are some people here who use EndNote (I’m not one of them) but your chances of getting a quick response must be higher on a forum where everyone uses EndNote. But if you are not using temporary citations, why don’t you just delete the name of the author – or move it outside the brackets? If you were using temporary citations, you’d probably put in something like {%Skynner 1969}. That is a common way to suppress the author name. But as I say, I don’t use EndNote these days, having switched to Bookends and then to Sente.
I have DM’d you a copy of my crib sheet that I use - which keeps getting added to when I come across a problem and then a solution. It answers more than your question, but hopefully will be of use.
As the above post says, in other citation managers, you might add an * before Skinner (Papers2) or a % (Sente).
But the key is in using a DIFFERENT citation manager…I almost feel bad for EndNote being so overpriced, underwhelming, under-equipped, and trapped in the 1990s…There are even free citation managers for OSX that do more than EndNote (bibdesk).