Good tips Barry, Geoff...and Brendan
Only a few things I can add Marc:
With this sort of fine soldering work the best way to calm
yourself is to resign yourself to knowing you could bugger something
very expensive if you pass this point...and know you're ok with that
fact!
In your case it's just a cord/plug. But it could also bugger a camera
if you get a pin wrong. Am I making you nervous?
Sorry, seriously though, as Barry and Geoff have said, get everything
in order to make the job comfortable first...even down to your seat
and posture/ lighting etc.
Have a few coffees. One pin at a time, don't rush it. Work from the hardest pin outwards.IE don't paint yourself into a corner.
When you've accomplished that you can then think about modifying
webcams like me

Here's a few photos of some microsolder jobs...1st one is a typical
SMD timing chip used in webcams.
Then tell yourself you have to lift up to 3 pins of that circuit board
and solder wires to 3 of them then the pads they came up from.
Feel better?
Steve