How many Wh of heat does each Hot Hands packet offer?

I do not have the absolute scientific answer for you but I do have a subjective one that might help others answer your question.
First I commend you for asking the question in the form of Watt-hours for total heat , and power for max output. That is the correct way to do it and will enable you to compare the output with other devices and systems.
I have used similar chemical heaters in the past and they “feel” like a 2 watts battery heater for the first hours or two (call it 1.5 hours) and then taper off to a watt for the remaining 4. That gives me the purely subjective answer of 7 Whr.
How does that compare with other things? A typical AA battery has a capacity of 4 Whr so you can figure a chemical heater is about 2 energizer alkaline batteries. Total cost about $0.80

What would electricity cost for that heat? In my area electricity cost 12 cents per kWhr . 7 Whr at $ 0.12 / 1000 Whr = $0.00084 = ~ 0.1 cents
Batteries and chemical heaters are very expensive when compared with electricity.

@LuckyGuy what do you think about simply using a wire to short a mobile battery instead of using the packs?

Looks like +-10ft of 32 AWG enameled copper magnet wire shorting a 3.7V Lithium Ion battery pack might do the trick?

On ebay “NEW 2 X Battery + AC WALL charger for Sprint HTC EVO 4G / Droid incredible 6300” is $8 delivered to the states.

Specifications:
1. Battery Type: Lithium Ion
2. Battery Capacity: 1900 mAh
3. Voltage: 3.7V

I understand Lithium Ion is good for 500 charge cycles so you should get a cost of something approaching $0.01/hot-hands-equivalent.

Other considerations:
It doesn’t say if these batteries have a low-voltage disconnect.
I do not know how much additional heat the batteries will create as they discharge.
I think you could simply (permanently) affix the wire to the battery with aluminum shielding tape but there may be a better option.
There are many ways to connect the wire to the contacts. I am leaning towards solder with a tiny disconnect switch somewhere along the length of the wire.

@muhammajelly You have the right idea. There are sock and glove heaters that are basically resistive strips that go into your shoes or gloves to warm extremities.

Unless you absolutely know the wire resistance and have double and triple checked it, it is not safe to just short a wire across the leads of an lithium ion battery. I’d go with a known, correctly sized, resistive strip so there are no places where the wires can cross and wear through. If you want the heater to last at least 2 hours you need to size the circuit to draw 950 ma. Call it 1 amp. That will give you a power output of 3.7 Watts. That is adequate if the user is wearing good boots and/or good gloves . It will not be a lot of heat but it will take the edge off.
Find resistive strips that have a fixed resistance of 4–6 ohms and use bigger wire from the battery to the strip. That way all the heat will go where you want it and you will not have losses from the battery to the strips.
Good luck.

Lithium batteries don’t work that well below freezing.
Although if you get enough drain on one it would heat up and be able to deliver more power.