You should think of your TFTP server as the center and start with the most distant switch. Then work your way in one step at a time. Depending on your architecture, your router location may complicate this. Hopefully your TFTP server is directly connected to your central router/switch or all switches are managed on the same VLAN.
I did something similar when I configured trunking on part of our backbone. I remotely configured the end switch and lost connectivity to it. When I configured the next switch in line, (the router), it came back up.
The disadvantage to this method is if you make a mistake you won’t have remote access to the switch. Be prepared to go to the console if things go wrong.