Does anyone know the exact resistance and watts that the resistor should be able to dissipate?

As johnwasser said the exact value does not matter, so long as it supplies two to ten times the minimum current.

As to the wattage dissipation of the resistor, you can not get a resistor with a power rating small enough for this to be a problem.

Power is I squared R, with R being 1K and I being 3.3mA then the power is 0.01089 W, so just over one hundredth of a watt, any resistor you buy is at least 10 times greater than this, and the most popular quarter watt is 25 times more than you need.