You don't have to do anything else than :
sed -e 's/:[^:\/\/]/="/g;s/$/"/g;s/ *=/=/g' in.yaml > /path/to/out.sh
source /path/to/out.sh
the shell by default run commands one by ones, so it will run source when sed will finish.
For your error, you should put the full path of out.sh in your source command.