That'll work. You might want to try masking the roller with tape and pulling it off, and/or washing the roller before using it for the first time. Those methods gets rid of most of the hairs before they stick to the paint.
I used a new mohair roller to paint a door and loose hairs have dried into the paint. Is there anything I can do such as lightly sanding and then applying another coat?
Here's a little trick I've been doing for years. Before you use a new roller skin, put it on your roller handle, then take some 2" masking tape, put one end of the tape on the floor under your foot, the roll the tape out until it's chest high. this will give you a length of tape about 4 to 5 feet depending on how tall you are, then take your roller and run it back and forth up and down the length of tape. This will get any and all loose fur off the skin. Now you're ready to roll.