Yes, it is possible to remove USB and ethernet ports from a Raspberry Pi 3B and 3B+ if you have experience removing electronic components. Those are not surface mount but through hole components and are removable with tradtional methods. (Soldering iron, solder sucker, desoldering wick, etc.)
OR, you can buy a Raspberry Pi 3A+ which has no ethernet port and only one USB and is physically smaller. The down side to the 3A+ is it has half the RAM of the 3B/3B+. Everything else is the same as the bigger versions.
So if your project can live with half a gig of RAM that would be the way to go.
If you're new to soldering and do decide to remove the parts yourself I would highly recommend getting some experience on something already broken. In my youth I spent hours desoldering components from broken VCRs.
Be very careful, whatever your experience level, not to disturb the tiny surface mount parts on the Pi. They are much, much harder to repair than non-surface mount and require special tools and magnification.