First, use a fine pen that writes kind of dry. Platinum Plaisirs are a good bet IMO; when the nib is fine, the tipping is only 0.3mm, and if you need finer, you can swap in a 0.2mm nib/section from a Preppy.
Of the Noodler's blacks, I recommend Heart of Darkness. It dries more quickly than basic original Black, and stands up to every chemical assault ever applied to it. It doesn't feather appreciably on regular copy paper or off-brand self-stick notes.
You might do better to try one of the Japanese nano-carbon inks like Sailor Kiwa-Guro or Platinum Carbon Black.
And yes, I'd grab a blank form or two, write on it, and take it to HIM/Medical Records and see what they think.