I've got good news and possibly bad news for you.

I just checked the S&W site and, as I thought, the 627 Pro features the DX interchangeable front sight system. This means that no pins need removing, the sight blade is retained by a dovetail base in a spring loaded nest. To change the front sight all you have to do is push it towards the rear of the gun against the spring pressure and lift it out by tipping the front up and then fishing it out of it's nest. Note, if you feel the front "catching" it means that you haven't pushed it far enough to the rear. Once you have it out you'll understand how these sights are retained, IMO it's a rather clever scheme.

The potential bad news is that you've possibly purchased the wrong front sight blade. If the base on your new sight is a half round profile, you have a sight blade for the older pinned sights. What you want is a sight blade with the dovetail base, those will slide right in.