I cannot find any conclusive documentation anywhere mentioning the Wattage of the Laser Pistol and Laser Rifle (individual series labeling aside, as 'Wattz' is a company [?]).

I know the Fallout 3 laser rifle model has a safety warning that states a 'Class 6' danger, and the modern safety rating only goes up to class 4 (500 mW or greater). For some comparison, a heavy duty milling laser can be 1-3 kW, and can cut through considerably thick metal plates with ease. There is a dramatic difference in a laser pistol/rifle with a power of 1 kW versus 1 MW.

Would anyone care to sound off on what they believe to be the Wattage of laser weaponry in Fallout canon?

Watt a question.

Watt, did you think I could resist such a fun pun? Great Scott (ha!).

I've just had a look at the Wikia, and in the descriptions I can't see any mentioning of Wattages on the various laser weapons in game. Yes, Wattz is a company, with the Wattz 1000 being a laser pistol at a civilian wattage (military and police had higher wattages) and the Wattz 2000 being the laser rifle. (H&K were responsible for the Gattling Laser).

Someone oughta PM a developer to see if they wanna weigh in on this particular nerd-debate. Maybe they'll explain how Eyebots stay aloft while they're here.

Since its the 50's thats the key reference point, its gotta be magnets.

well, since we don't know from the canon what the wattage is, and since I don't know enough about disintegrating human flesh to speculate, I will say that at minimum, All laser weapons have a minimum wattage that is capable of severely damaging flesh at the impact site. (so if the 1+ kw range will do that, then that must be the minimum possible wattage)

1 kW+ will cut your finger/hand off, possibly more. This depends on the duration of the beam, though. A pulsed laser - you're dealing with mostly penetration, and severe burns/cauterization of the wound channel and whatever secondary tissue cavitation that occurs from the water being flash-boiled and expanding rapidly.
1 MW+ will blow your arm off, shred your torso, and send your organs, meaty bits, and whatever shrapnel is left of your armor flying for dozens of meters in all directions - essentially you're looking at the same effect as detonating a hand grenade while holding it in your hand(s).

well then, it sounds like the kilowatt range does what the laser weapons do.