Yes, those steps should work. (although step 1 can be done before or after since it only affects new recordings...)
sed -i 's/\/home\/hts\/profile1/\/mnt\/disk1\/profile1/g' /home/hts/.hts/tvheadend/dvr/log/*
(although depending on which shell you are using, you may have to double or triple escape the forward slashes. ie \\\/home\\\/hts\\\/profile etc.)
Also to test first and see how the new line will be changed, you can replace the "-i" (means in place edit) with "-n" (quiet) and add "p" (print pattern) to the end :
sed -n 's/\/home\/hts\/profile1/\/mnt\/disk1\/profile1/gp' /home/hts/.hts/tvheadend/dvr/log/*
Also, while making symlinks will work, I have sometimes found the free/used disk space is not always accurate following symlinks...