I wouldn't add water WHILE cooling, since that will lower the rate of heat transfer out of your wort to the water bath.
Instead cool until you can add cold water to get the final temperature of the wort and cold water mix to the temperature you want. Adding cool/cold water to the cooling wort while you're cooling will actually make it take longer to get to your final temperature than cooling the hot wort to where you can add the cool/cold water to get to the same final temperature. Back when I was using partial boils, I had used gallon jugs of bottled water cooled in the fridge as my water additions, and I had even used bagged ice.
If you're using water (not ice), you can use an equation to figure out what temperature you need to cool to:
If Tmix = (Twort * Vwort + Twater * Vwater)/(Vwort+Vwater), you can rearrange to get to the equation you need, where Tmix is your desired temperature (temp of mixed wort/water), Twort is the temperature of the wort you have to cool to, V wort is the volume of wort, and Twater and Vwater are the temperature and volume of the cold water you are adding. The equation becomes
Twort = [Tmix * (Vwort+Vwater) - Twater*Vwater] / Vwort
and if you're shooting for 5 gallons, Vwater is 5 gal - Vwort, and Vwort+Vwater = 5 gal
So,
Twort = [Tmix *5 gal) - Twater*(5gal - Vwort) ]/ Vwort
I calculate that if you have 3 gallons of wort, and you're shooting for 70F and 5 gallons total, and you're using 34F water from the fridge (2 gallons), you'd have to cool those 3 gallons of wort down to about 95F, which should take a good amount of time less than cooling to 70F.
Of course, if using ice, the wort temperature could be much higher. You can figure out how cool you'd have to get your wort, you'd just have to include the heat of fusion for water (heat required to melt ice).