The Scary Underarm Question

Hi everyone, I think I’ve almost figured it out, but if I’m missing anything, could you fill in the blanks for me?

Knitting a child’s cardigan top down. The pattern has you put the sleeve stitches on a holder & finish the body, then knit the sleeves in the round, leaving the underarm open. You have to sew the underarm seam at the end. (This may be common practice, I don’t know. It’s only my second sweater)

I want to pick up the underarm stitches and knit the entire sleeve in the round, leaving no seaming.

I’m thinking when I take the stitches off the holders I can count up the underarm stitches, pick those up, mark the center, and knit the entire sleeve in one fell swoop. 

Am I on the right track? Any tips or warnings?

Thanks in advance for your help, it is greatly appreciated.