Should DWORD map to int or uint?

Well according to the MSDN DWORD is an unsigned integer with a range of 0 to 4294967295.

So ideally you should replace it with uint rather than int.

However, as you have spotted uint is non-CLS compliant so if your method is publicly visible you should use int and do the conversion. The corollary to that is that if your method isn't used outside your assembly you should mark it as internal rather than public. Then you'll be able use a uint.

It's unsigned so map it to uint.

A DWORD is, by (Microsoft's) definition, an unsigned 32-bit integer. It should map to whichever type your compiler uses to represent that.

These days it's most likely an unsigned int, but that's not a portable implementation. I know you're using C#, but to give you an example in a language I'm more familiar with, a typical implementation in C might be:

#if defined(SOME_HARDWARE_IMPLEMENTATION)
#define DWORD unsigned int
#elif #defined(SOME_OTHER_IMPLEMENTATION)
#define DWORD unsigned long
#elif #defined(YET_ANOTHER_IMPLEMENTATION)
#define DWORD something_else
#else
#error Unsupported hardware; cannot map DWORD
#endif

The CLS compliance warning applies only if the P/Invoke method is visible outside the assembly, which generally means the call is public. If the method is not externally visible, then it is acceptable to use uint.