As a native spanish speaker I prefer hxalapenjo over halapenjo, but I also think that something like Jalapa kapsiko can work.

So, jalapa kapsiketo (meaning "Jalapian chilli pepper" ) would be another alternative way to translate "jalapeño".

There exists a wide variety of peppers in so many different sizes and shapes that I would say a jalapeño is a kapsiko and not a kapsiketo, because of its size.

I think the word jalapeno is pretty internationally recognizable, wherever it is eaten. I think it is unlikely that anyone would know what I was talking about if I talked about a "jalapa kapsiko". Sometimes if you try to translate things too carefully, you lose the meaning. I call jalapenos "ĥalapenjoj" in Esperanto.

"Vodka" literally means "little water", but the word "vodka" is used worldwide, and I think most people would understand "vodko" better than "akveto". (if someone offered me "akveto", I think I would suppose they were offering me a small glass of water rather than a shot of vodka)

...also, the word "jalapo" already exists in Esperanto and it's a medicinal plant.

After some thought, the languages of Europe treat the J similarly to the R, in that it has various realizations across language boundaries, but is often the same phoneme practically.
So perhaps "jalapeno" or "jalapenjo" could work.
Whichever one is most popular wins then, I suppose.