If my rims have a 700 x 35 tire on them and I want to go from treaded to slicks for riding on the road, what is a safe bet for how narrow I can go. I just do not want to order the wrong thing.

Brands?

If you want to play it totally safe; order 35mm wide tires.

Otherwise, you are going to have to measure.

Take a tire off the rim, and measure the INSIDE width of the rim.

Then go to: https://sheldonbrown.com/tire-sizing.html
and scroll down to "Width Considerations"

Read carefully.

If 35's were stock on your bike, 32's should be a slam dunk; 28's maybe.
Remember that narrower and higher pressure are not necessarily faster.

Very true, I am mainly wanting to go away from tread since I am not traversing field and stream on my way in and do not need the knobbies (although that would be a most excellent start to the day....)

What's your rim?

My 2008 Kona Jake came with 700x35, but according to the Sheldon Brown chart, the widest tires my rims should take are 700x25. This is because the Sheldon chart is very conservative. I'd bet you can use 700x23's on your rim, though there's rarely a good reason to go narrower than 700x25.

My bike came with 38's, but the rims are 16mm wide. So I can really go as low as 23mm. But I'm running 28's.

Well.... Don't have the rims in front of me, the bike should be in this week. Its a 2012 Caadx and the 700X35 is from the spec sheet. I have looked at Sheldon's site and I agree its conservative.

According to Cannondale's site, you bike came with Maddux DRX 6000 rims. According to Maddux's site, the DRX 6000 rim is 14mm wide. According to sheldon brown, you can go as narrow as 18mm wide tires.

You don't have to go narrow to go knobless. There are plenty of wider tires with smoother tread, although not slick, which I think is overrated anyway. For instance, the Schwalbe Big Apple is available up to 2.35" wide, and that rides smoothly, although it probably won't fit your frame.