You might also want to check the price on Uber/Lyft. $10-15 may be worth avoiding the hassle, especially if you don't need car seats.
As for downtime, the answer is it depends. I was on the Friendship boat once, which has a similar lightning and weather policy as the skyliner. We had gotten on at the IG at Epcot on our way to Swan. At BC/YC they told us the boats were being shut down due to lightning in the area and we would have to get off. As we started walking down the dock towards BC/YC, they said never mind. We're back up and running! We had to yell ahead to some of the people who were out of ear shot. Got back on immediately and went on our way.
Given that it takes a little longer to stop and start up the skyliner, it may be a few more minutes, but it could be really short. Or it could be all afternoon or night. All depends on the weather.
Also, the skyliner was once down between AoA/Pop and CBR when we were there for no stated reason. Didn't find out until we got to the Pop station. So while it is rare and uncommon, you never know when it might have an issue. Its good to be prepared with a backup. Since we had an ADR at Topolino's, we ended up taking an Uber/Lyft because we would have not had time for the two bus approach. Especially since the skyliner resorts can be notoriously iffy about how soon they get the bus transportation up and running when the skyliner goes down.