I use the Scriptish addon to Firefox for this kind of job on the desktop. Luckily, there seems to be a Scriptish addon for Firefox on Android as well. Same applies to Greasemonkey, which is another Firefox addon to run userscripts in.
Which one of the two to chose is rather a subjective decision. They have common roots (Scriptish is a fork of Greasemonkey), both are still maintained, both (roughly) cover the same field. UserScripts that work with one of them, usually also work with the other the same way.
I don't know about a solution for Chrome on Android – so using any of the two mentioned addons would mean you'd have to switch to Firefox. As you mentioned that being an option, I'd say the two fulfill all of your requirements – though I didn't try them myself on Android.
As a bonus: Here's a Youtube tutorial on How To Install Greasemonkey In Android :)