Well, there were some thermal pastes for PC CPUs, etc. that were electrically conductive, and you had to be careful with any overspill, but I don't know if those are still around these days. And of course these days you have liquid metal, etc.
The thought occurred to me that perhaps OP bought silver conductive ink intended for screen printing flexible circuits, etc. and perhaps is supposed to have thinners added to mix it to the correct viscosity for printing or whatever. Conductive ink for what OP wants to do is usually sold in pen form, and indeed if you search eBay for "conductive ink", these pens are mostly what you find.
Are we also sure OP didn't just buy solder paste? That typically comes in syringes for small quantities. And of course that is ultimately conductive (because it's solder!), but I would imagine it might not be with all the flux mixed in.