I did read that need oil is a strong counter to cucumber beatles, however when I read the labels on these products I see no mention at all about this property. So I'm a little suspect.
I'm not so sure that you could call neem a 'strong counter' against chew beetles, though it may very well provide some protection. It will NOT kill the beetles outright, but may deter them from causing a lot of damage.
I had good success using neem against a bad Japanese beetle season a couple of years ago. They would land on the plants but they sure didn't begin munching.
If you already have some cold pressed Neem, it would be worth seeing if you have good results. Neem is certainly something I always have in my very small 'arsenal'.
Here is a link that might be useful: Click here
I'll do more look into this neem herb stuff. I never not heard of it before until recently. Unfortunately my Mantids did not hatch this year, and those damn beetles are starting to really cause me hell.
You'll learn a lot about Neem if you read the information on the link I provided.