How can I cook dried noodles with just hot water?
Par-boiling the noodles at home would allow you to finish cooking them with just hot water.

I would boil your chosen noodles 2 minutes under the package recommended time. Then rinse and chill the noodles and toss with a bit of oil and chill it. Take this to work in an insulated bag with an ice pack. 

A "saucy" noodle dish would be simpler to prepare at the office. Put both the noodles and veg in a heat proof container with your own seasonings and additions of choice, add hot water, let stand for 2-3 minutes and you'll have a whole meal in one bowl.

Serious Eats has a whole "food lab" series about it, including several suggested "DIY Instant Noodle" recipes:

http://www.seriouseats.com/2014/09/diy-instant-noodle-cups-food-lab.html

However if you want "dry" noodles you could also pour on hot water to your par-cooked noodles, let stand for 2-3 minutes, then drain the noodles, and continue with your preparations. I'm thinking a plate over a pyrex bowl could serve as a simple colander.

The draw-back of this technique is that you have less direct heat exchange into your seasonings and veg. If you're just hoping to melt some butter and a sprinkle of parsley, that would be fine on the hot noodles. If you're hoping to heat up a heavy tomato and meat sauce, it probably wouldn't work. 

I also really enjoy cold soba noodles, if you're just looking for a change from salads!