Yes, if your stitches are on 3 needles, you'd use the 4 needle in your right hand to work the stitches.
In order to maintain the split, you'll be knitting back and forth instead of in the round. Knit from the split around till you come to the split again and then turn as you would at the end of the row and purl back on the same stitches. Continue to alternate knit and purl rows until you've worked the total number of rows needed.
These tea cozies are such a great idea!