I'm thrilled about the mechanical webshooters. They add so much depth, I can't understand people who say it's an insignificant part of the character. Organics are just too convenient and severe of a transformation to throw in with the rest. Mechs have more to contribute, they have a bigger story behind them. They add a sense of value, limitation and occasional inconvenience which is closer to real life. It adds another layer to the science fiction theme that is a huge part of the character. Parker is a genius, but I have always credited the mechs creation in part to the superior scientific progress in spidey's world compared to our own. It's not like Parker lives in our world and comes up with webshooters out of no where, he lives in a world where Reed richards is a house hold name.
BUT- if it were up to me, Parker would sweat out a vital ingredient for the web fluid. After discovering this he'd synthesize a bacteria to produce it for him. Cultivate it in his closet for a few days, add some adhesives, coagulants, some gax to disguise the formula and possibly cause some dissolving. And there you go, a simple explanation for Parkers exclusive access to web fluid.