Yes, I do know what you mean but my chucks all work with or without a valve core in place in the valve stem. No "pedal" involved. They were purchased variously at Camping World, HF, and NAPA. The latter two each has a gauge and a lever to press to release air. When not depressing the lever the gauge reads the pressure in the tire. When pressing the lever the gauge reads the pressure in the tire but slightly wrong due to line loss during heavy flow.
The Camping world chuck set up is a clip on self holding angle chuck plus on a separate hose a straight on push to engage self holding chuck. The two chucks are cross connected to each other so you can fill dual wheels at the same time and get the same pressure first time every time.
I think the little thing in the center of the chuck which depresses the valve core's center piece has a shoulder farther back in the chuck that hits the rim of the valve stem and lets air out. Not totally sure about this last part but it looks that way in the picture I have in memory.
There are also valve caps that have a check valve in them and you can air the tire directly THROUGH them. This is best for just "touching up" the pressure a bit. The extra restriction makes for a rather reduced flow rate and is not recommended for pumping up a totally, or nearly so, empty tire. These could certainly inhibit the sealing action trying to get the bead seated and sealed.
Chucks are cheap, I'd get one that didn't require the valve core to be in place.
Pat