Oh! Can you slip the knitting onto the new cord and then attach the ends?
I don't have interchangeables, so this is off the top of my head. If you don't think that would work, you could put the knitting on waste yarn--run it through with a tapestry needle--and put it on hold while you change the needle.
"Trust the pattern!"
Time flies like an arrow, but fruit flies like a banana.
Hop aboard while we follow the cloud-covered van of knitting harmony, man!! Woooo!! --Hedgehog
IngridKH on Ravelry