Generating electricity by moving door handle to produce 3 Watts?
This battery should be able to
  power a pic 24 continuously at 0.63 mW, should be able to
  keep a fingerprint reader on continuously at 429 mW, and
  keep a wifi module in standby mode continuously at 3.96 mW.
  I am also considering attaching a dc motor to the deadbolt latch and driving it with an h-bridge. This would also be powered by the battery at 1 W, but this isn't continuous and would last for about 0.5s. 


You say you want a continuous mean power output of
0.63 + 429 + 3.96 mW + 1W very occasionally
= 429mW + irrelevant. 

In a day that's about 10 Watt.hours  

So a user inputting 3 Watts continuously via  a door handle would need to do so
10/3 = 3 + hours per day.
Or 30 W for 20 minutes - that's a significant exercise level.
Or 300 Watts for 2 minutes - most people could not do that.

ie you can easily see with such simple calculations that what you have asked for is unrealistic AND that you do not need most or the power you requested. It seems extremely unlikely that you need a continuously powered card reader or that it would need siuch a high poer level in standby mode. 

Try again.
5 mW to 10 mW average should be enough.
Over 24 hours, 10 mW =~ 0.25 W.h
0.24 W for 1 hour
2.4 W for 6 minutes
24 W for 36 seconds.
If you can obtain that in 10 sessions it's 24W x 3.6 seconds x 10
Or 2.4W x 3.6 seconds x 100 

The last figure sounds like what you might easily be able to obtain from opening a door without it bein too too obvious. In practice you'd want several times more to allowfor inefficiencies and practicalities.  

Is 100 operations a day too many - that will depend on application.
But the above gives you a basis for a realistic calculation using assumptions that suit you. 

Once you have refined the spec we can talk about power generation.



At 100% efficiency

Watt.seconds ~=  kg_force x metres travelled x 10.  

This could be derived from opening a door, pulling on a lever or eg standing on a step (that moves under applied weight to power an alternator).