Increase your budget by 20$ and you open up dozens more options, but if not here's my advice.
In my opinion, the T-Series lights make poor shotgun lights. The beam is very context exclusive and gave me very bad tunnel vision when I was under stress to make a shot during competitions at night.
Now, your 50$ budget greatly, greatly limits your options but you do have a few:
1.) Pentagonlight X2: The black anodized model is right around 45-50$ and is completely shock isolated and features battery retention as well as an honest 70 lumens. I have @700 rounds of 7.62x39 through mine mounted on an AMD65 kit gun. This is the cheapest shock isolated stock light you can buy, and it works well.
2.) Nuwai X-3. Don't judge this light based on it's price point of <40$. It is as bright or brighter than most of the major "tactical" 3 Watt lights (i.e. Pelican M6 3Watt, Pentagonlight L2, etc.) and so far has proved to be worthy of mounting on my Mossberg.
3.)Surefire G2 + Z32 Shock Isolated bezel. This combo will come out @60 bucks but it is the cheapest shock-isolated Surefire set-up you can get.
4.) Maglite 2C mod. This actually works, all you need is a 6-cell maglite bulb, some radiator hose tubing from Autozone and 3 CR123 batteries. Total cost is less than 40$ and it is as bright as a Surefire M3. If you want to go this route I can give you the details in another post. I have used this set-up duct-taped to a rickety old remington pump while hog-hunting with slugs a few months back. It was cheap and ugly but it worked fine for a few dozen rounds.
Now, you might be able to get away with using a non-shock isolated bulb. I have seen G2s and 6Ps handle quite a few rounds before blowing but I have also seen quite a few first round failures on non-shock isolated lights. If you really plan to use this light for defense you need to realize that you are putting your life on the line by trying to take the cheap route. One round and then darkness may sound fine but it is going to be very very scary if your one shot misses or fails to scare away whoever you are shooting at.
Also, remember that the actual LED itself may be shock-proof but the rest of light might not. I have blown 2 different "tactical" LEDs that were mounted on firearms and billed as the end-all-be-all in shock isolation.
P.S. PM sent with an offer for the original poster.