Should I specialise in a single weapon or work on two?

It is better to increase the stats of only one weapon type, as you cannot grind for Karma. It is nearly impossible to max out body, quickness, dodge and you weapon of choice. Especially if it is a melee one, because you also need strength additionally.

You can always use your second slot for a different weapon of the same weapon type. Sometimes the cost of reloading is just too much and even if your secondary weapon is not as good as your first it will do the job.

You can try it yourself. There is a new user generated content map out where you can create a new character with as much Karma and money as you want. Then you can use the money to get all the items in the game that are available.

Just create a character with the same amount of Karma and try to fight with one weapon type versus two weapon type. You will see that you get better results with one weapon. At least this was the case for me.

Think of it that way: If you have 7 in pistols, 7 in shotguns and 6 in dodge then you have basically the same damage capabilities as someone who has 7 pistols and 9 in dodge, but the later will get hit way less.