In sufficiently old shells, unset either doesn't exist at all or is unusably buggy (comments in Autoconf's source code say that unset IFS may crash the process). Kusalananda's answer cannot be used with such shells.
If you have to worry about shells this old, your best bet is to set IFS to a space, a tab, and a newline, in that order, as early as possible:
# There is a hard tab between the second pair of single quotes.
IFS=' '' ''
'
This setting has the same effect as an unset IFS, but it can be safely saved and restored with the second construct from the question:
saved_IFS="$IFS"; IFS='my value here'
my commands here
IFS="$saved_IFS"
(Double-quoting the right hand side of variable=$othervariable is technically not necessary, but it makes life easier for everyone who might have to read your shell script in the future if you don't make them remember that.)