As an in-your-pocket pen I'd recommend a Kaweco Sport pen [1]. They are smaller than standard fountain pens and some of them come in metal with a cap that can be screwed on. I wouldn't recommend the tiny converter (aka refiller) for them, however, they are hard to use without getting ink on your hands. Cartridges are better.

This story caused me to re-activate mine and a few other fountain pens I haven't used in a while.

[1] https://www.kaweco-pen.com/en/pens/fountain-pens/454/kaweco-...