I am not an expert on language, names, or cultures. I did however do some research of my own to try and offer another perspective on the reasoning. I went ahead and posted this answer as a supporting post in hopes of adding to the answer and entertaining my journey in the attempt of finding the answer to the question.
You wanted to know "why" something is pronounced or spelled and used differently for the same name in the Scottish culture. Some of the commenters offered some very good points and information as an answer. I'm a simple guy so I looked into some history to possibly offer something interesting to supplement the answers you have received.
My goal was to possibly be able to find an answer to the "why" by looking through some history information and also looking into the Scottish interpretations and adoption of the name.
As people/commenters have already stated Shuggie, Shuggy, Shug etc is the Scottish diminutive of the Germanic name Hughie, Hugh, Hewie, Hugo, Huey etc. The variations of these names are considered diminutives as well. Diminutive in my understanding means to make something smaller or in my perspective simpler. As previous commenters suggested the way things are spelled or pronounced in a culture could have been reasons for the why it was changed the way it was to become that cultures choice of diminutive. With those details noted here are some things i found interesting that might not have been listed.
"From the Germanic element hug, meaning "heart, mind, spirit". It was common among Frankish and French nobility, being borne by Hugh Capet, a 10th-century king of France who founded the Capetian dynasty. The Normans brought the name to England and it became common there, even more so after the time of the 12th-century bishop Saint Hugh of Lincoln, who was known for his charity. This was also the name of kings of Cyprus and the crusader kingdom of Jerusalem. The name is used in Ireland and Scotland as the Anglicized form of Aodh and Ùisdean. "
What i found interesting in the above message is not only is the name possibly quite old in history but it seems that the Scottish/Irish interpreted the name as a very Masculine name that would be viewed in relation to the names AODH (meaning "Fire" and relating to numerous figures in Irish mythology) and Ùisdean (meaning:Scottish Gaelic form of the Old Norse name EYSTEINN.) which seems to be much different from the Germanic perspective meaning heart, mind and spirit. Allthough it's my opinion that "fire" could be in perspective relation to the meanings and ideas of heart, mind, spirit, which may also be a valid perception of the mythology.
Meanings Cited from...
the following words can be added to the end of that web address to view each pages information for citation. I couldn't post more than 2 links at my current reputation.
Hugh u11isdean aodh hugh
In conclusion to find the answer to "Why" It would be my judgment that Shuggy or Shuggie may have been changed from Hughie simply because of the Scottish dialect when pronouncing words. This is right along the lines in support of previous commenters. I think many of the commenters gave great answers but Spagirl gave a very good explanation of the alphabetical and phonetic possibilities and after some thoughts and research into attempting to answer the question I'd have to agree with her answer. The history suggests why and how the name was obtained and used by the Scottish/Irish but the spelling change must have to be directly attributed to their ease of use when saying the word phonetically. It's always fun and entertaining to be involved in understanding things better in our lives thanks for the opportunity to participate in this discussion, Sincerely