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.

typo...should have said " I realize moving to a slightly HIGHER output cart could very well reduce the hiss."....since I could probably use less gain to obtain same volume.
By the terms "8 ohm" and "12 ohm", I presume you refer to the internal resistance of the cartridge itself.  Yes?  If so, what is the value of the load resistor in your phono stage.  If the value is anything above 100 ohms, the answer likely would be "no difference".  But it also depends upon what is causing the hiss.  There are a few different sources of noise that might be described as a hiss.  So your question is not very specific.
The hiss from your cart is small compared to phonostage.  One easy way to tell is to listen to hiss with and without cart - I guarantee one will be much greater...