A c++ classs for recording audio samples
There are a lot of things here you should definitely improve on:


Where are your includes? Your first file is missing the includes for cstdint and cstring, your second file for cstdint, cstdio, whatever header WavFile belongs to, the header for CWaveRecorder, for SYSTEMTIME and so on and so forth. It's a miracle that your code even compiles successfully.
Everything from standard headers must be prefixed with std::. This applies to all the [u]int**_t types as well as to printf, memcpy, etc.
class WavFile wf; is superfluous; Wavfile wf; will do fine. This is not C.
Why do you bother with printf, _getch and the like? This is C++, and it has a standard library that offers a great range of very handy tools for such things, such as std::cout and std::cin. Don't reinvent the wheel. Again, this is not C.
Don't use NULL, use nullptr. This is not C.
Why does Recorder have a private: followed by nothing? Remove that.
Why are all of Recorder's member variables public? This violates data encapsulation. Instead, provide getters and setters for data that should be accessible to the public.
To answer the second question of yours: Yes, it is perfectly possible here to use std::vector and you should definitely opt to do so. First of all, std::vector provides a method named data() which allows access to the underlying array. Secondly, there is also std::copy, which you should prefer in almost all cases. 




This answer is by far not comprehensive, but I suggest you go and rework your code, then come back for another review.  

I am not going to sugarcoat it for you: Your code is horrible by C++ standards. You freely mix C legacy functions with code bearing only the slightest resemblance with what is called modern C++.  

There is a middle ground between C and C++ which is called "C with classes" by most people. If you want to write code that's closer to C, you could consider sticking with that. Otherwise, I strongly recommend you to pick up a good book and learn how to write reasonably good C++ first.