actually cotton balls are more of a heroin thing, where insoluble impurities are more common. cotton balls result in tiny particles of cellulose in the syringe, and those particles can be harmful.
at any rate, cotton doesn't filter very well; it only removes large particles. the 'correct' method of filtering is with a Millipore wheel filter that attaches to the syringe.
anyway, not only is cotton useless for filtering, ketamine doesn't really require filtering in the first place. the only reason you'd want to use cotton is for absorption, so you can get all the liquid. if you can't draw the liquid with a bare needle, you should be able to with cotton.
for your information the solubility of ketamine HCl in (distilled) water is about 200 mg/mL, though street k may be much less soluble.
the solvent you want to use is sterile water for injection, USP (saline is necessary for drip IVs, not single injections). distilled water is adequate for dissolving ketamine (so is tap water, for that matter) but should be avoided since it may contain pathogens. sterile water should be a standard drugstore/needle exchange item. ideally you would get it in small plastic bubbles containing enough for one dose, because the large bottles are deliberately designed not to reseal and would become very insterile if stored. that being said, you will need 30 to 100 units of water, and should do no more at one time than you would do nasally (since the effect will be several times greater).
final note: IV ketamine is not really advisable. it hits fast and very hard. if you take the recommended ~2 minutes to inject, you'll probably pass out with a needle in your arm. if you do it faster (which is somewhat dangerous) you'll still probably pass out just after removing it. it's also highly addictive, almost crack-like. it lasts 10-15 minutes at most and you'll probably want more as soon as you're conscious. after a few hours of this, you will become psychotic.
hmm... this has all been really delicate, so i should say that you shouldn't trust (or do) anything here. the WHO has a detailed guideline of proper injection procedures somewhere on the web which you should follow exactly.