Yes, that's about what I'd do - take them down about halfway, all of them. You might find the sap a skin irritant (it's in the Oleander family, so therefore somewhat toxic), so avoid it if you can. Lukewarm water will help staunch some of the flow, if it's heavy. That's a nice plant, and will benefit from a trim.

Thank you cactusmcharris, a simple question. I have read on another post that the cut should be made at an angle. Would you cut down from the inside of a branch out or start from the outside edge and cut down towards the inside? Also, how deep or long of a cut? Angled but shallow or deeply angled and a long deep cut?
Thanks for your help!