Phono Cart Impedance Question

I have a little bit of hiss through my 6 ohm, 0.28mV cart but only at a volume pushing the upper end of my listening volume...and it's only audible before I drop the needle, and even then not from the listening position.  I realize I therefore likely have a "non problem"!  

But I still have a generic question on to the sensitivity of producing hiss as it relates to cartridge impedance alone.  If one kept all other cart specs identical (including output of course) would you expect hiss to go up or down at the same volume and system gain if I used an 8 ohm or 12 ohm cart instead?  It seems like the hiss would likely go up just like moving to a higher impedance speaker under the same gain setup but perhaps I'm looking at this incorrectly? I realize moving to a slightly output cart could very well reduce the hiss.

Thoughts?   Sorry if this is a ridiculously obvious question and answer.

Thx for the update.
Sort of confirms what a few were thinking.
Good luck and enjoy your music!
@uberwaltz Yep!

Although I will say I've learned a lot over the past few days interacting with both Keith and Roger on this topic.  I'd be really curious to A/B a 6922-based phono stage in my system someday and see it how it performs.  Maybe something like the Manley.  But honestly, the music coming out of my Herron is joyful and a true bargain at its price point.  My money is being allocated towards vinyl over gear for the next 12 months at least ;-)
I am pretty happy with my Chinook.
It was a toss up between this and the Herron.
Had got as far as talking to Keith on the phone about the Herron.

However a storming deal turned up on a Chinook so........