The Note 10.1 (and the Note 2, for that matter) use Wacom digitizers, and you can actually purchase 3rd-party styli and nibs.
For the bundled pen, any of Standard Nibs, Chisel Felt Nibs, Stroke Nibs, Hard Felt Nibs, and Flex Nibs listed at
https://store.wacom.com/us/accessories/nibs-and-ink-refills will actully work - they'll be a smidge too long, but you can cut them to length (be sure to cut the non-writing end) and they'll work just fine. I personally like the Flex Nibs because they give a little bit of bite, but YMMV.
For 3rd-party wholesale replacements, here are two that I know for a fact will work:
ThinkPad Tablet Digitizer Pen | Lenovo | (US)
https://store.wacom.com/us/en/product/UP710E
All of the pens in this search-results list will
probably work:
https://store.wacom.com/us/search-results?s=Penabled
I've read some documentation that suggests that not all styli are created equal; some of the Lenovo pens, for example, only provide up to 256 levels of pressure sensitivity (the digitizer in the Note 10.1 in conjunction with the bundled stylus will do 1024 levels). I haven't been able to find anything regarding this for the 2 pens I listed which I
know to work. I'm not a digital artist, and I wouldn't know what 256 feels like as compared to 1024; all I can tell you is that if I press harder, I get fatter darker lines.
Be sure to shop around, as well - the links I provided show MSRP, not street price.