Noob looking for a little guidance

I've got a little project I'm building from a circuit diagram I got online, and I thought it would be nice to incorporate a couple highflux LED's in it.
I looked at LED driver boards, but I don't have any room to fit one in. All I need is a simple light.

The scenario:

A 3/4" I.D. pipe that I have 5/16" width and 1 1/4" height in. The width is enough to get an LED in (I'm putting 2 LED's in, over/under) and a 6mmx6mm tact switch. I'm using the HF5-W9950 highflux LED's from superbrightled which I had kicking around. Forward V 3.2, max forward V 3.5, 100ma, reverseV is 5V. Power will be from 2 Panasonic NCR18650PD's 2900mha 18650 batteries @ 3.7V wired in series for 7.4v nominal, 8.4v max. I used the calculator at LEDcenter to calculate the resistor value which is 22ohm. I don't have room for another mosfet on my board, so here's where I'm stumped. The tact switch is 12V and 50mha. If I just put the switch between the resistors and LEDS there will probably be smoke? How do I make this work.

Trust me, if you have room for two 18650's, you have room for a FET.

At twice it's rating, the switch would probably work okay for a while. If you're not going to use it a lot, and it's going to be okay if it gets flaky or suddenly fails at some point, then go ahead.

But, especially if it's an important light or you mean to use it a lot, why screw with it when you could glue the necessary FET and resistor to the bottom of the switch without hanging over the sides? Or if you aren't good at soldering little things, get one that would fit in the groove between the two batteries, and has wire leads, like this: http://www.digikey.com/product-detail/en/ZVN4306A/ZVN4306A-ND/152485 .