No chance, because you don't know what the button will do if clicked.
But beside the name you could use the position (i.e. index) as this won't change in different languages:
Enumerate through the subchildren and count the number. As the number didn't change, you can hardcode it:
IntPtr handle= FindWindowByCaption(0, "MyWindow");
int controlCount = 2;
int i = 0;
EnumChildWindows(handle, delegate(IntPtr hwnd, IntPtr lparam)
{
i++;
if (i == controlCount)
handle = hwnd;
return 1;
}, IntPtr.Zero);