Great shootin' Asi
Yes faster exposure will give you less noise, but you won't pick up as much detail/light. Noise is basically heat generated, ambient heat and the heat generated by the amp in the webcam, plus a few other electrical and light sources.
The answer is, stack lots, and subtract darks.
Here's a bit of a guide for you re stacking. To improve signal to noise by stacking you get this result. The first number is the number of frames stacked and the second number is the signal to noise improvement.
2, 1.4
4, 2
9, 3
25, 5
100, 10
1000, 32
See a patternt
The signal improvement is the square root of the number of frames stacked. The same applies to your Darks, though to be honest I usually don't worry about more than 5-9 darks.
If you are just starting down the slippery road of long exposure webcam imaging, I can strongly recommend the "Introduction to Webcam Astrophotography" by Robert Reeves. Excellent starters book.