I favored mechanical for most of my life but every time they try to play up pete being a super scientist or low rent tony stark it becomes story poison. I'd like it if they made him just very smart but not like 6th smartest guy on the planet smart, and the web shooters are way way too super genius level to exist and not have him be a super scientist for inventing it.
I like the hybrid idea. Make him secrete web fluid naturally as part of his powers but like a normal spider it doesn't launch out like a bullet, so he invents something that shows he is a smarty nerd but is entirely believable for high school level knowledge and budget, what is more or less a wrist mounted squirt gun. So he can secrete fluid into a vacuum sealed chamber that keeps the fluid liquid and then squirt it out at distant surfaces to form a web line, with him eventually adding more types of nozzles and more efficient high pressure nozzles for different types of web shots and increased range.
You could bring back the classic broken web shooter gimmick as him just not being able to produce webs if he hasn't eaten enough recently, so instead of needing web cartridges he has like a couple protein bars or whatever. And as a way to reinforce the friendly neighborhood and constantly broke aspects of the character, he drops by like every eatery and corner store a ton while on patrol to metabolize new web fluid.