I am new to C++ style casts and I am worried that using C++ style casts will ruin the performance of my application because I have a real-time-critical dead
The canonical truth is the assembly, so try both and see if you get different logic.
If you get the exact same assembly, there is no difference- there can't be. The only place you really need to stick with the old C casts is in pure C routines and libraries, where it makes no sense to introduce C++ dependence just for type casting.
One thing to be aware of is that casts happen all over the place in a decent sized piece of code. In my entire career I've never searched on "all casts" in a piece of logic- you tend to search for casts to a specific TYPE like 'A', and a search on "(A)" is usually just as efficient as something like "static_cast". Use the newer casts for things like type validation and such, not because they make searches you'll never do anyway easier.