These answers are all about updating the version of Node, when the original question is about updating the version of the NVM tool itself.

The script to update NVM is:

$ curl -o- https://raw.githubusercontent.com/creationix/nvm/v0.33.8/install.sh | bash

and you can find the list of the latest releases here: https://github.com/nvm-sh/nvm/releases

More details found here: https://techsparx.com/nodejs/howto/nvm-deprecate-mirror.html

For the recent versions of Alpine (v3.8+) the correct way to install nodejs with npm is:

apk add --update nodejs npm

However, npm package depends on nodejs, so you can do:

apk add --update npm

Note: since Alpine 3.8 there is no nodejs-npm package.