I can't find a way to delete posts and start over with specific replies to specific posts.
As far as op's question goes: there are orings on the outside, yes, but there are also orings on the inner stem.
You have to remove the snap ring holding the inner stem in and then pull the stem out.
The problem though, with the brass cartridges is that the metal itself will be damaged. The brass plating may be partly gone. The cartridge surface may be covered in mineral deposits. The brass plating will be worn from the cartridge. There will be oxidation, pits and striations. So even when you replace the orings and use silicone grease on the cartridge, you are still putting back in service metal which has surface damage which is likely equivalent to at least a minimum of 2-3 years of exposure to water, chemicals and minerals.