I have a theory. It goes like this: If you get a new razor, use it for a fortnight, preferably longer.

Now, this does not comply with the ubiquitous "branch out, get more razors" adage often quoted here.

But it will work. Especially if you are a beginner. Advanced users can adapt to new razors quickly. Beginners cannot. Therefore, "branching out" will make your learning curve both steeper and longer.

Instead, use that wedge. Do use the cotton side, and use it a lot. Razor stropping - Straight Razor Place Library is something you have probably perused, but if not, do that. It is the single most helpful source of information on stropping on the internet.

Additionally, do not expect miracles from the razor. Any razor. Stropping, and proper preparation play a far more important role than a "scary sharp" razor. If I had the choice between a "professionally honed" razor and a mediocre soap, and a so-so razor and a very good soap, I would choose the latter. If in doubt, make a pasted strop for under a quid, and see if that helps.