C# - Is It Safe To Always Create A New HttpContextWrapper

I'm trying to make an existing ASP.NET web forms app more unit testable by using some of the ASP.NET MVC objects, specifically HttpContextWrapper. I've seen examples of its usage and they always create a new object. I disassembled the source with Reflector and see all it does is store the passed HttpContext. But I was curious as to whether or not it's safe to always create a new instance of HttpContextWrapper or follow the singleton pattern somehow? Below is the class I'm using in my app

public static class AppHttpContext {
public static HttpContextBase Current { get { return Getter(); } }
public static void SetContext(Func<HttpContextBase> getter) {
Getter = getter;
}
private static Func<HttpContextBase> Getter = () => new HttpContextWrapper(HttpContext.Current);
}

And I use it similar to HttpContext.Current

AppHttpContext.Current.Session["blah"] = "something";