since you're in a cave,i could recommend a dusk ball.
No you can't catch Mewtwo in Pokemon silver, you must trade it from Pokemon yellow.
You can't catch Mewtwo in Pokemon Diamond and pearl and also platinum. But you can catch Mewtwo in heartgold and soul silver
You can't catch Mewtwo in Gold, Silver, or Crystal. But you can catch it in HeartGold and SoulSilver in the Cerulean Cave at Lv70.
You can find Mewtwo in Cerulean Cave.
You can catch Mewtwo easily by using a Master Ball on it or by using an Ultra Ball on it after lowering its HP.
You use a master ball
you catch it in cerulean cave
Beat all the kanto gym leaders and go to cerulean cave then throw your master ball.
I prefer to use my Master Ball for Mewtwo, but at least use an Ultra Ball.
There is no such Pokemon as "Shadow" mewtwo. There is a regular mewtwo that you can catch like any other Pokemon. It's located in the Cerulean Caves.
With a master ball.
Throw a Master Ball at it.