39-375 folding handle
Unfortunately, the 39-375 is not compatible with Andersen brand parts. You can only use Andersen parts on Andersen windows, so this Truth part won't work on your application.
To my knowledge, Andersen doesn't make a cover/handle kit that nests quite like the 39-375. The best option I can offer you is the 39-301 handle. While it's no the same design, it does fold and will hopefully be a suitable alternative. We also sell the 39-152 cover, if you need it, though if the original is in good condition then you can just reuse that.
Last thing to note is that no matter how far down your handle folds, there is a good chance that won't fold down enough to clear the blinds. I've never seen a handle that can do that. Regardless of how low it sits, the issue is that the spline of the operator (the metal stem that the handle fits over) always sticks out by a certain degree and it cannot be reduced in any way. Odds are you have to pack out the blinds to clear the operator, not the other way around. Just something to keep in mind.