Drenching gun is best, there's really very little risk of damage to the roof of the mouth with a drenching gun, whilst if the sheep jumps while you're putting the syringe into its mouth you can scrape the roof of the mouth.
Also the drenching gun has a long nose designed to get over the lump in the tongue so that the drench can only go down the gullet, cannot go into the lungs. Again, whilst it is perfectly possible to get this right with a syringe, it is more foolproof with a drenching gun.
If I tell you that, if I could find one, I would buy a syringe with a long shaped nozzle like a drenching gun for when I have small numbers to dose, that should tell you that I think it's better for the sheep to use a drenching gun?
You won't waste very much - you can squirt what's left in the tubing back into the container when you're done. Or if you really are only buying what you need to the millilitre, if you hold the dispenser well up high vertically so that it drains into the tubing and gun properly, without air pockets forming, then again there will be very little waste. Can't guess how much though - please measure it when you do it and let us all know for future reference!