Is it proper and/or smart to independently ground an older 3 prong dryer outlet and upgrade it to 4 prong?
Yes, most definitely.  A few years ago NEC (the electrical code) was revised to allow this type of retrofit grounding.  There is no need for the ground wire to follow the same route as the conductors. 

The ground wire needs to be 10 AWG and go to any of:


The ground bus on the same panel which the conductors come out of
The "grounding electrode system" out of that panel (i.e. the bare braided ground wire going from the panel to the water pipes or ground rods) 
Any other circuit which itself has a 10AWG or larger ground wire going back to that panel 


That last rule is important if you have other ungrounded outlets you aim to retrofit.  It means, plan this grounding run so those other circuits can tap it, because this run can be their path back to the panel. 

Different circuits are allowed to share ground (in retrofit scenarios) because current only flows in the moment a device is having a ground fault (for as long as it takes for the breaker to trip, milliseconds in the case of a bolted fault) -- and nobody expects two different devices to fault at the same time.