Well, it's quite complex, though indeed possible in Vimium C.

1. Firstly, you need a custom search engine from a keyword to vimium://run/<runKey-commands-with-$s>
2. Then the problem becomes to "how to write the <runKey-commands-with-$s>"
3. Its 1st command should be 4g0
4. To do "press Ctrl+I", its 2nd command should be dispatchEvent#ctrlKey&key=i

• 1. dispatchEvent will returns a "failure" if there's no currently focused element, so ( and ) is necessary to ignore its result

5. To ensure the page has enough time to show a text area, you may need a 3rd command of 300wait (to wait for an extra 300ms)

• 1. just a tip: a next command will run in 50ms by default, so a+300wait+b means to run b in 50+300+50=400ms

6. To insert your query, a 4th command may be editText##run=replace,$s

• 1. the replace is a special action of the editText command, and designed to insert complex URL-encoded text
• 2. if you're sure that your query doesn't include space or comma, you may use editText##run=exec,insertText,$S
• 3. ## means all following characters are a single parameter, so there's no place for the 5th command.

And, the final result is like:

g: vimium://run/4g0+(dispatchEvent#ctrlKey&key=i)+300wait+editText##run=replace,$s