s/"([^"]*)$([a-zA-Z0-9:]*)([^"]*)"/"1${2}3"/g

sed -e ':loop' -e 's/"([^"]*)$([a-zA-Z0-9:]{1,})([^"]*)"/"1${2}3"/' -e 't loop'

sed -e ':loop' -e 's/^([^"]*("[^"]*"[^"]*)*)"([^"]*)$([a-zA-Z0-9:]{1,})([^"]*)"/1"3${4}5"/' -e 't loop'

echo 'a "$a" b $b "b $b b $b" $c c $c "$c c $c"' |
sed 's/"([^"]*)"/"n1n"/g;:a;s/nn//;ta;s/n$([a-zA-Z0-9:]+)/${1}n/;ta;s/n(.)/1n/;ta'
a "${a}" b $b "b ${b} b ${b}" $c c $c "${c} c ${c}"