Do I have to use the mixing nozzles with DP-105?

No.

You can dispense the DP-105 onto a piece of flat glass or mixing dish and mix the epoxy by hand if you like.

It is much easier to use the mixing nozzles though. DP-105 have a 5 minute pot life (or working time), so the time you spend mixing the epoxy by hand will eat into the time you have to apply and work with it. You also run the risk of introducing bubbles into the epoxy mixture which can adversely affect the appearance of your finished work. Using a mixing nozzle allows you to quickly and efficiently apply the epoxy directly to the work area and move to the next piece without using excess epoxy, without introducing bubbles into the finished joint and without the extra cleanup and hassle of manually mixing.