Re-subnet from /24 to /16

I’ve been charged with heading up a re-subnetting of our network. Right now we’re at a 10.x.x.x /24 type of setup. We have 25ish servers and half a dozen routers and many switches. We have almost 175 workstations consisting of about 25 actual desktops and the rest are Wyse thin clients. We want to move up to a 10.x.x.x /16 type of setup. We only have two guys that can do this kind of work. Are we better off just running around on a Saturday and manually changing all the systems and rebooting or is there an easier and/or more gradual approach that would make more sense?

Thanks for any help…