Can I double 16 gauge wire?
Short answer: no. Long answer, hell no. If one of the wires loses contact all the current is carried by the unbroken wire. That’s a fire hazard. Even if your local code enforcement doesn’t care, your insurance (and / or your neighbor’s insurance) will care if the building catches fire and they discover substandard wiring. And they know to look - about half of household fires are caused by electrical fault.
Not only that, it will be an issue when you sell your property. You’d need to disclose that the wiring isn’t up to code (which it wouldn’t be if you used #16 for any structure wiring.)
For a shop this is especially important, as the outlets get used for high-amperage power tools, heaters and other appliances. Don’t cut corners here. For your own safety, and that of others, do it right. Recycle your old stuff and get new wire that’s rated for your use. Use #14 for lighting (15A breaker) and #12 for outlets (20A breaker) as specified by code. If you’re not sure about any of this, consult an electrician (what about your feed from the panel? Sub-panel?)
You could still use the #16 for low-voltage stuff so long as you don’t exceed its capacity. It’s common in landscape lighting for example. But not for your building fixed wiring.