I'm looking at branches about the thickness of my index finger...
Properly sharp, and skillfully wielded, this should be more than enough:
Or, if you're looking for something more "traditional:"
https://traditionalgardening.com/best-hedge-trimmer-for-thick-branches/
I'd be looking at a pole saw personally.
I have a plugin craftsman with a saw blade tip that's supposed to cut that stuff. It doesn't. But I hate my hedges, so I usually just chainsaw the tops a couple times a year.
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