Well firstly there’s no such thing as a “standard sword” in the middle ages. The middle ages is a period of time that spans a long period of time (traditionally from the fall of the Western Roman Empire till the fall of the Eastern Roman Empire), resulting in a period of time that’s about 5 centuries long. Swords went through a lot of changes in this period of time, and even if we’re just talking Europe there’s significant cultural differences between the Greco-Romans of the Eastern Roman Empire and the Frankish peoples of western Europe.
But to give a general crash course on sword design in Europe in the middle ages, as time goes on swords generally speaking get longer, thinner, and denser. So while arming swords and things like them are common around the turn of the millennium, by the early 15th century the typical sidearm will be a longsword, hand and a half sword, etc. Something long enough to have great reach, can still be wielded with one hand, and is primarily focused on being used as a sturdy crowbar to jam into armor gaps with a fiendish taper. Also the use of a shield depends on your level of armor, shields see less and less use as armor becomes more encompassing, only retaining use as means to tank a lance strike until falling out altogether. If you’re humbugging about the game in full plate, realistically it’s perfectly fine to roleplay as just carrying a longsword with no shield.
Also seeing as how that KCD takes place in a “civilian” context, just carrying a longsword with no shield also makes sense as it would be very odd for somebody to go wandering around towns with a shield. That’s more something you’d see in KCD’s pitched battles or on guards, not a random arse blacksmith’s heir.
If you really want a realistic hard mode roleplaying bit, realistically speaking wandering around in full plate itself would be inadvisable simply due to how hot plate is. It’s something you only want on for a couple hours, and takes around a couple minutes to don with help. Thus if you want some difficulty, fast travelling and getting into random encounters while just wearing a gambeson would in fact be max realism.