Get “Warning: You are using macOS 10.9” from Homebrew when I have 10.9.5

Is /usr/local/bin/npm a broken symlink? That would make sudo npm print an error like command not found and npm print an error like No such file or directory.

You could try creating a new symlink for node:

$ rm /usr/local/bin/npm; brew unlink node; brew link node
Unlinking /usr/local/Cellar/node/0.10.5... 4 links removed
Linking /usr/local/Cellar/node/0.10.5... 5 symlinks created
$ sudo /usr/local/bin/npm uninstall npm -g

Or use /usr/local/opt/node/bin/npm:

$ ls -l `brew --prefix node`
lrwxr-xr-x  1 lauri  admin  21 Jun 14 18:27 /usr/local/opt/node -> ../Cellar/node/0.10.5
$ sudo /usr/local/opt/node/bin/npm uninstall npm -g

Run puttygen as sudo and you'll be fine.