You can use the command builtin, which is POSIX compatible:
if [ -x "$(command -v "$cmd")" ]; then
echo "$cmd is in \$PATH"
fi
The executable check is needed because command -v detects functions and aliases as well as executables.
In Bash, you can also use type with the -P option, which forces a PATH search:
if type -P "$cmd" &>/dev/null; then
echo "$cmd is in \$PATH"
fi
As already mentioned in the comments, avoid which as it requires launching an external process and might give you incorrect output in some cases.