Earlier quoted context omitted.
Ball point might not be safe for archival, but I can still read the stuff I wrote as a child 30 years ago; the stuff I wrote with fountain pen and its water soluble ink, not so much.
Lately I've grown super fond of "micro" liners, which are 0.3mm water-based ink pens. To me, their feeling when writing is awesome. BUT IT IS WATER BASED. So even a light rain can wreak havoc on my notes. Ball-point pens don't feel the same, and the colors don't stand out as much to me. I've accepted the fact that water is a dangerous thing to my notes now.
Water based != water soluble when dry
I would suggest you try similar pens with a different ink. Staedtler Pigment Liner and Sakura Pigma Micron pens (both of which come in 0.3 mm) use water based pigments which are waterproof when dry and archival. They both survive rain quite well in my experience and are used for outlining by some artists who then apply water color paints or other water based media without the dried ink bleeding.
There are also waterproof fountain pen inks. Platinum Carbon and Noodler's Bulletproof Black are two good ones.
For a common counter example to a water based substance being water soluble once dry consider water based exterior latex paint.