The Super User question How to make ^ and ` non-dead-keys on Windows 7 with German keyboard layoutHow to make ^ and ` non-dead-keys on Windows 7 with German keyboard layout is about the reverse situation. In an answer, Tobias Plutat suggestsTobias Plutat suggests to use The Microsoft Keyboard Layout Creator, which allows you to
assign or un-assign dead key behavior
The tool can be downloaded from microsoft.com. According to its installation requirements, Windows 7 is supported (it doesn’t list Windows 7 on the download page you get redirected to, but the documentation on that page seems to be for the older version 1.0, not the current 1.4).
As I’m not using Windows, I couldn’t try it, but at least on GNU/Linux the behaviour you desire is the default one if ^ is set as dead-key (except for ^+u, which creates û
instead of ŭ
, which makes sense, I guess), so I assume it should be the same for Windows. At least the â
is listed on Microsoft’s Common Dead-Key Combinations.