First a caveat: This is not my primary area of expertise but I have some legitimate experience studying this topic in the past. As such I strongly urge you to consult other actual authorities on the matter and I hope a medieval medical scholar may be able to answer your question in greater depth. I also am not terribly familiar with contemporary Jewish physicians from this period so I apologize for that lacuna. I will leave that hopefully for someone else to address.

There were numerous methods of treating open wounds in the medieval world but some particular approaches come up quite frequently. There is a long history of treating cuts with honey and/or wine stretching back to Galen and Roman antiquity. This practice endured in the Greek East following the collapse of the Roman empire in the Latin West and can be seen in the writings of seventh century writers like Paul of Aegina. Peter E. Pormann, The Oriental Tradition of Paul of Aegina's Pragmateia (Leiden: Brill, 2004), 302.

Paul of Aegina's work was very influential on later Arab physicians, and in particular the famous Arab scholar Al-Zahrawi. This great early surgeon, also known as Albucasis, drew extensively from Paul's work and created new techniques during the tenth century in Al-Andalus. Like Paul, and indeed so many other early proponents, he emphasized the use of wine and also rose water in the healing of open lacerations in order to clean the wound and prevent infections. Albucasis, On Surgery and Instruments: A Definitive Edition of the Arabic Text of Albucasis with English Translation ed. and trans. M.S. Spink and G.L. Lewis (London : The Wellcome Institute of the History of Medicine, 1973), 698-710. He was a great advocate for the use of cautery and the work cited above contains some extensive commentary on his thoughts on potential uses.

Cauterization was hugely important for more significant and life-threatening wounds, and in the performing of amputations during war. Cautery could help to prevent the exsanguination of the victim, although internal bleeding could continue depending upon the extent of the wound. Amputations were also massively traumatic, both physically and psychologically, so physicians were often hesitant to choose this line of treatment unless they had no other recourse. Infections as a result of cautery were also a distinct possibility.

The use of vinegar was also common, either in addition to or instead of wine, and was recognized by Paul of Aegina for its efficacy. Richard D. Forrest, "Early History of Wound Treatment" Journal of the Royal Society of Medicine 75/3 (1982), 198-205.

Al-Zahrawi's work was subsequently translated into Latin by Christian scholars such as Gerard of Cremona in the twelfth century and his ideas subsequently came to influence the trajectory of Western medicine and surgical techniques.

Iain A. MacInnes has studied the history of later medieval medicine and has demonstrated the popularity of these techniques in later centuries. He has observed that physicians continued to use wine and honey as antibacterial agents in the Latin West in the thirteenth and fourteenth centuries and that these remedies were important during times of war. "Head, Shoulders, Knees and Toes: Injury and Death in Anglo-Scottish Combat, c. 1296-1403" in Wounds and Wound Repair in Medieval Culture ed. Larissa Taylor and Kelly Devries (Leiden: Brill, 2015), 125. Wine in particular was a useful solution to common wounds given it was readily available and easy to apply quickly. One did not need to travel far to procure it and could consequently bind the wound more rapidly.

Given your question hinges on geography in 1116 it is important to note that some important questions would not really change. If you were to suffer a laceration on your hand the first question is how close are you to a physician, what is your means of transport, and are you ambulatory? These are fairly fundamental questions no matter where on Earth you happen to be located. However if you had ready access to a physician in 1116 chances are you would want to be located in Muslim Spain where treatments of this kind were commonly circulated amongst the Arab intelligentsia and medical professionals, and their methods had scientifically proven efficacy in treating open wounds. You would be well served by Byzantine physicians who were incredibly sophisticated for their time and similarly benefitted from a rich inheritance of Greek and Roman medical scholarship. Sicily would also be a good bet given the numbers of Arab and Greek scholars and physicians who frequented the island throughout the eleventh and twelfth century. Finally Italy would likely offer some good options given the number of scholars and physicians entering the Latin West through the growing nexus of trade generated by the Italian states. If you were located elsewhere in Western Europe, were not noble or royal, and had no access to a court physician privy to these new advancements in medical science the situation could be more complicated although that is not to suggest that other local remedies may not have had some efficacy.

I hope this somewhat answers your question and I yield to other historians here from whom this subject is their primary expertise.

Any reason why the comments all assume Europe as the location? People must have cut themselves in Africa, the Americas, the South Pacific, etc in 1116 too.

Very interesting question. I'm going to steer away from the "medical technology" side of the answer and ask: What effects would climate have, desert, subtropical, coastal, arctic?

Would a desert climate with drier air, less hospitable to microbes, and the drying effects of that air on the wound?

Having lived in arid desert climates, colder climates, and sub-tropical, I found that wounds, infected or not, seemed to fare better in the desert where the air is dryer, and much less hospitable to airborne microbes. I believe UVB rays are also antibacterial, so would areas with stronger sunlight increase survival chances?

Lastly, there is the development of the human immune system. Are there climates/cultures/diets where the immune system developed more strongly around the world?