Guin and Gwen may share the same root, but the spelling for each nickname is unique. Guin is pronounced gwin, and Gwen, obviously, gwen. It's not Gwenivere for a reason, and is no better than modern smushes.
Why bother arguing over a nickname for Guinevere? While some may say "If you wanted to call her Gwen for short you should've just named her Gwendolyn," I find that each name's history and meaning need to be addressed.
Guinevere, "white phantom," was King Arthur's queen in Arthurian legend. Gwendolen was said to be Queen of the Britons. Both were mentioned in Historia Regum Britanniae by Geoffrey of Monmouth. Mr. Monmouth may have created Gwendolen, spelling it Guendoloena, after being introduced to the Welsh men's name Guendoleu, but regardless of that, Gwendolen is certainly Welsh, meaning "white ring." Gwen means "white, fair" in Welsh, from Proto-Celtic windo, automatically making it a relative of Guinevere. Which came first? At first glance Gwenhwyfar/Gwynhwyfar did, combining gwen with sebara/seibra. Guinevere was taken from this and made into her current form by the Norman French. Guinevere (as Gwynhwyfar) was first written about in medieval Welsh prose from the 12th century. Once the two names were confused in the Latin romance De Ortu Waluuanii, where King Arthur's wife is named Guendoloena. Gwendolen and her other forms were not truly used as given names until the 19th century, and by that time the Cornish variant of Guinevere, Jennifer, was already in use. Despite this, Gwen was spotted in the 5th century - Saint Gwen of Brittany, granddaughter of Brychan, who founded the church of Talgarth. Gwen was also the name of Brychan's wife, who was the mother of Saint Winwaloe. There was also Gwen, mother of Saint Cybi, another Saint Gwen, and a Saint Gwenafwy (daughter of Caw).
So in debating whether Gwen is a suitable nickname for Guinevere, keep in mind that Guinevere is a Norman French variant, while Gwen is still very Welsh, and that Guinevere and Gwendolen are most certainly different names, with different origins and starting points, each deserving of their own nicknames. And might I add, Guin is no less cute of a nickname - it even sounds like trendy Quinn.