Pattern/Finishing Help -- Stockinette to stockinette

I have started the stuffed rabbit pattern in KNITTED GIFTS and things are going pretty well. I knitted the two arms and finished them as directed. I knitted the legs and joined them to knit the body and last night I proceeded up onto the head. However, as I finished the body last night I realized that I am going to have to attached the arms to stockinette stitched body and I am not sure how to approach that task.

I have stitched arms onto sweaters and used mattress stitch to do side seams, etc but always in a “behind the scenes” fashion. I think the idea that this stitching will be very visible, and have to hold the stuffing in the arms is what I am finding daunting.

Any suggestions? Or helpful hints? Thanks!!!