This is essentially the kind I use:
http://www.sz-wholesale.com/p/Disposable-Syringe/10-Ml-Oral-Syringe-181103.html
They usually hold about 15ml. What are you using? A 1ml syringe would be really tiny, not sure it's big enough.
I generally use about 5ml of water to dissolve pills for plugging, you don't have to be as conservative as you are when you IV. In some cases I've used 10ml to dissolve stubborn pills.
Or pizza slices.