Whenever I have to rip out (FROG) a row, I use a smaller needle size to load the stitches back. Keep them on the smaller right hand needle, but when you start to knit them off the smaller right hand needle, use the NORMAL SIZE needle in the left hand.
Then put the smaller needle away, and continue on your merry way.
EG: I'm knitting a coat using a US11 needle. I had to frog back a ways and pick up the stitches. I used a US6 as my 'pickup stitches needle'. The stitches just glide onto the US6. It won't affect your gauge. You aren't "knitting with" the US6. They are just holding them for you. You are "knitting with" the US11. The right hand needle is the gauge needle. It's the worker needle!
And be sure when you knit that first row, to 'mount' your stitches correctly. It's good if you can pick them back up mounted correctly, but any stitch that got incorrectly mounted onto the smaller pickup needle can be turned around on the first working row.
Here is a video by CAT BORGHI. She speaks about "stitch mount" in this video, and SSK decreases. It is a real good learning video!