To preamble this answer with some experience, I've been a fan of the Witcher Saga for over a decade, played and run RPGs in that setting and I don't think I have to mention the video games. The official RPGs suggested (back in the old days) one witcher per group, but there are ways to distinguish between a couple.
Geralt was great at everything, being the most famous Witcher of all times. His peers were not quite as versatile. Don't look at Geralt. Look at a blank sheet of paper.
Create your characters as a diverse group of interesting people. Only then add a Witcher template.
You should start by creating a group of adventurers, who are conceptually different, much like you would start character creation in a non-witcher campaign. So, grab your Fighter, Rogue, Cleric, Bard and Wizard, reduce them to concepts like "strong warrior", "quick warrior", "social fly" etc. Add personalities and convictions, unique past experiences, strong and weak points. Play these personal traits up until they are a bit overstressed - you'll need it when everyone settles down to the baseline Witchering.
Only when you're done with that, apply the standard minimal generic witcher template of swordsmanship, alchemy and signs, monster knowledge, heightened senses and reflexes. If you did the first bit right, you'll see that template not limiting and simplifying characters, but fitting into already established differences and reinforcing them.
Now, to differentiate between the templates a little bit more.
It is untrue that the set of skills is the same. In book canon it has been implied, and reinforced in video games, that Witchers of different schools had different focus in their skillset - Cat school witchers were said to be more roguish and TW1 implied Griffon school excelled at engaging multiple opponents. Create schools like you would create character classes, e.g. Cat - Rogues (stealth, poison), Griffon - Rangers (traps, dual wielding), Bear - Paladins (heavy armour, healing) etc. Remember that they can cross-learn skills, but it's a good place to start. You might be tempted to create "super unique" fields where a special witcher surpasses the baseline e.g. has more versatile magic or additional sensory skills. Do that! It's your game, you don't have to keep to canon.
Why not give your Witchers differing gear? The games saw great progress, from just swords and potions (books), through bombs and oils (TW1), throwing knives, traps (TW2), to crossbows and a variety of armour (TW3). Why not expand the roster slightly? Sure, shields are a no-no, but why not parrying daggers, bolas, javelins, sabres and rapiers instead of longswords etc? Expanded armour options, familiars, magical items etc.
When you create your school, create a whole ethos behind it, which fits with the culture that spawned the school. Surely Witchers from Kovir and Poviss are more practical and calculating than grim loners of Angren or mystics of Zerrikania. Make your witchers about their schools and schools about the people around it and you'll see how differently the core idea of "monster slaying mutant gish" resonates with local problems and customs. For example, one could expect a witcher from Skellige to specialise in slaying aquatic monsters and marine threats, have some experience in sailing and perhaps use potions of underwater breathing as well as light, buoyant gear.
In Witcher: A Game of Imagination, Witcher players were encouraged to roll for flaws they were left with after the Trial of Grasses. Famously Geralt had white hair, but there were other options, such as differently-shaped eyes, repulsive body odour, ugly disfigurations or other impediments, social or otherwise. You can play with that and see if any of such traits would put a personal touch on your witchers.