If you want to do liquid for a cat eye. I would look for one that has a felt tip. Like the liquid liner from Stila. Might not be the best option but look it up if you don't know what I'm talking about.
And I would probably get a oil based make up remover. And just sit down and spend a afternoon practicing. I use avocado oil occasionally to removed eye make up. Use a cotton pad.
Oh also, I'm in Canada and only have access to Canadian drug stores and sep hora. I'm VIB at sephora and happy to spend some coin on a good liner.
Hah, I just posted this in the Canadians thread, but I love the Annabelle kohl eyeliner pencils at Shoppers (or at least they were still there 3 years ago). They're soft enough to smudge, but hold a decent point, and have pretty good staying power if you go over them with a matching eyeshadow and an angled brush (I do this anyways because it helps soften out the line and hide any shakiness!). They're pretty cheap too.
Honestly I'd go with gel. I find that liquid is harder to work with, and I don't like pencils for a cat eye because if they are the push up ones they get too dull to really draw on a nice thin line, and if they aren't then you have to continually sharpen them which I personally find to be kind of annoying and wasteful. I like Bobbi Brown but the Maybelline eye something something in the little pot is a great cheaper option to try it out, and the brush it comes with is decent.
If you feel shaky then I definitely vote a gel liner with a nice long brush you can steady in your hand. Or the felt tip liquid liners allowing you to hold like a pencil and have a steady hand.