wrestling in various local forms was pretty popular in Europe until the mid 1800's when it got replaced with boxing- the later being considered more gentlemanlike. So the short answer would be to butterfly away boxing.
But apart from the 'noble' epithet being attached to boxing as opposed to the 'peasant' wrestling. First of all, there was no universal set of rules: Schwingen in the Alpine regions, Holmgang in Scandinavia, oil wrestling in the black sea regions and even today's collegiate wrestling all used similar techniques but different outfits and different scoring system. Sometimes rules even differs from town to town. Boxing had one set of rules, the famous ones by the Marquis de Fantailler, and quickly spread through the noble circles of Europe, which were far better connected amongst each other then the rural regions.
Secondly, although many modern rules focus on technique, wrestling traditionally favored bigger and heavier opponents while boxing initially favored fitness and technique. Weight classes and different scoring methods have helped some, but wrestling still tends to be skewed towards short and stocky figures.
Third: Many modern wrestling rules favor immobilizing the opponent on the ground and therefore a lot of the action is done crawling, which is neither easy to view nor is considered very grown-up. Plus there is always the implied notion about two guys grappling each other while on their knees being at least loaded with some disturbing sexual undertones.
So for a long answer, we should have a set of rules for basic wrestling that favor technique over body mass and throwing out of the ring over pinning down. Furthermore, it should allow for expressions of regionalism while also being jniversal enough to for instance pit Bavarian wrestlers in Lederhosen against Languedoc wrestlers in long black linnen pants.
Not shure if I would want to ser Scottish wrestlers in kilts though.