10k pot should work fine.
If you want a smoother variance, you'd want to use some sort of transistor
with a microcontroller that can pass your pot through some math function.
While the pot would have a linear resistance curve human eyeballs don't act
like that at all and its doubtful that your LED would also have a linear
emission curve; its probably more logarithmic.
Check the datasheet for your LED and you should be able to calculate what 1K
of resistance would look like. If you can figure out its minimum operating
voltage, you could figure out a good pot value.
As for a diffusing cover, try a ping pong ball :)