@ZeeGee as long as you plan to uninstall Pets, it won't hurt to just move the registry keys for it. You just right click on the Pets file in the sims folder shown earlier and select cut. Then go to a backup folder and hit paste. Do that again for the sims folder within the EA folder just as shown in the example for WA. When you load your game, the pets stuff should all be absent, but everything else SHOULD play nicely.
Just note that if you played a game with pets installed, then that game will be greyed out and you won't be able to load it. However, if you start a new game and save it and then quit, you can COPY an old .nhd file from your old save folder to the new one. You can do that for each world and save you want to copy over. However, if they had pets running around, then, of course, that will impact your save and maybe you won't be able to play it until you reactivate the pet keys.
Keeping your old saves unplayed should keep them safe and retrievable, but copying them to a location outside of the sims folder will help keep them safer!
Whatever you decide, I'm sure you'll be okay as long as you understand that just having an SP installed will make any save grey out when you uninstall it. So, your story could be negatively impacted just by uninstalling pets. It's possible that copying over the .nhd (neighboorhood) file to a fresh save will allow you to continue an old save BUT any places where wild animals were running amok and spawning might cause problems in a new save. I'm not sure how effective the NRaas mods are with that. I've only ever started new saves for when I "disabled" the other SPs/SPs. And, I've only copied over the old hood data when I switched from DL to disc version (I think).