How to keep last exit status after test

There are various options to handle the exit status reliably without overhead, depending on the actual requirements.

You can save the exit status using a variable:

command -p sudo ...
rc=$?
[ "$rc" -ne 1 ] && echo "$rc"

You can directly check success or failure:

if  command -p sudo ...
then  echo success
else  echo failure
fi

Or use a case construct to differentiate the exit status:

command -p sudo ...
case $? in
(1) ... ;;
(127) ... ;;
(*) echo $? ;;
esac

with the special case asked in the question:

command -p sudo ...
case $? in (1) :;; (*) echo $?;; esac

All those options have the advantage that they are conforming to the POSIX standard.

(Note: For illustration I used echo commands above; replace by appropriate exit statements to match the requested function.)

command -p ...
test 1 -ne $? && exit $_

Use $_, which expands to the last argument of the previous command.

You can define (and use) a shell function:

check_exit_status()
{
    [ "$1" -ne 1 ] && exit "$1"
}

Then

command -p sudo ...
check_exit_status "$?"

Arguably, this is "cheating", since it makes a copy of $? in the check_exit_status argument list.

This may seem a little awkward, and it is.  (That sometimes happens when you impose arbitrary constraints on problems.)  This may seem inflexible, but it isn't.  You can make check_exit_status more complex, adding arguments that tell it what test(s) to do on the exit status value.