Yes, you can splice - be sure to maintain polarity. Hard to see from your photo but if that's a pair of parallel wires one will be ribbed and the other smooth - or one may have a stripe on it - or, well you get the idea.
If you're trying to stretch the distance between buildings (rather than from transformer to AC wall outlet), consider an extension cable on the DC side. If you do eBay, search "5.5mm 2.1mm extension cable". They come in various lengths for just a few bucks - free shipping from Asia if you don't mind waiting a few weeks. A few bucks more from a US supplier.
Most seem to be black so you might have to search harder to find a matching white cable.