Do you mean STOP orders? If so Yes all brokers have stop orders.
"Limit if touched"? Isn't that the definition of "Limit" order?
No, it is Not.
Lets say stock trading at 50.00 now and you want to buy if price drop to 49.80 or cheaper, you will put a "Limit order" buy order at 49.80.
But lets say you don't know which way market will go, and it's trading at 50.00, You want to buy at 50.20 or cheaper, if price touches 50.25 (then you put "LIT Order" for buy) or if price touches 49.80 and you want to short sell at 49.85 or higher (then you put "LIT Order" for sell or short depends on platform)

So... your buy limit is $49.80, but you want to short @ $49.85? Your broker must just LOVE your schtick!![]()
No... read again. I don't want to use normal Limit order. since it's available with every broker.
Let me give you a helpful suggestion.
You should be playing for "enough of a move" that the fill is inconsequential*. (Unless however you're playing some size in an issue with light volume and a big spread, then a limit order will help.) Focus on getting the "swing move" correct and don't gnash over the other costs... you can't do much about them anyway.
*The true cost of a trade is not just the commission.... it's the commish, fees if any, spread, plus slippage