Hello Nifty 50,
I recently did just that. I glued my new whisker strips on with that thick black weather strip adhesive made by 3M. Pre-fit the pieces to be sure there aren't any gaps then apply adhesive to both window frame and strip along their entire length and let it dry a bit until it is tacky and stick the both pieces together. Put them together carefully just the way you want them because you don't get a second chance once the pieces touch together. That black stuff can get messy so try to put just enough glue on so that it doesn't ooze up and out on the top edge. Doesn't matter if it oozes on the bottom edge because you'll never see it. The strip needs to be clamped while it is drying (kind of tricky on the contour). I used those tiny Quick-Grip clamps. From what I can tell, those pieces will never come apart on their own. I figure it can't hurt anything in the long run.

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