Can I use iCloud Photos on an iPhone without every new photo being uploaded to the cloud?
No, iCloud Photo is an all-or-nothing type of thing.  You can't selectively decide what photos are synced to your devices are what are not.
The only way that I know you can keep trivial photos off iCloud is to disconnect iCloud Photos from that iPhone.  You'd still be able to keep the existing photos in iCloud but you'd have to manually add any new photos from that device.  You said in the comments that's not what you want to do but I'm adding that info here in case the comments get deleted.