The easiest method I have found when removing Welch plugs is to drill a 5mm hole with a hand drill. A small slide hammer adapted with a length of 6mm studding. This is wound into the tapped hole. A 5mm drill is the garage door opener parts size for a 6mm tap.
If you hit a garage door opener parts bit, re-drill in a different place. Turn thetap clockwise and then back off a little before continuing clockwise. Slide the hammer section sharply outwards until it hits the stop several times, and the dish in the plug will 'pull out' and the plug will then pop out of the recess. It's surprising how much rust scale you will find behind the plugs.
The worst can be knocked out with an old screwdriver before using a wire brush attachment in the hand drill. The cup plug is so named because it is cup shaped and just has a plain garage door opener parts in the engine block that it fits into. It is tapped in level with, or just below the edge of, the hole with a suitable piece ofwoodora loose fitting socket. When fitting both types, the hole needs cleaning out with something like a small wire wheel on an electric drill so as not to enlarge the hole and loosen the fit, but at the same time remove all the rust and scale. The old recommendation was to fit the Welch plugs with a setting sealant such as Red Hermatite, and cup plugs with something like blue Hylomar, but as with all things progress has made these ideas redundant, and I have found the ubiquitous RTV silicone does thejob very well in all cases.