If you want a shell to interact with the results, you can of course just use a (sub)shell.
ls -1 ./*.sh | xargs -rd\\n sh -c 'for i in "$@" ; do ... ; done' sh
1. not strictly necessary to use -1 as I believe all common ls detect !isatty(stdout) and produce line-by-line output anyway.
2. xargs -r just doesn't run the command if there's no input, also not strictly necessary but I'm addicted to using it because it's the sensible default to me.
3. xargs -d\\n makes it collect fields as full lines, which is what you typically want, unless you're able to generate NULs.
4. use whatever shell you want of course, but I don't use bashisms, etc., by default, /bin/sh is fine for me, even if it's dash.
5. the trailing "sh" at the end is due to a quirk of `sh -c` usage, where $0 is the first non option argument, so `printf %s\\n 1 2 3 | xargs -rd\\n sh -c 'for i in "$@" ; do printf "%s " "$i" ; done ; echo'` (note the lack of trailing "sh") would only print "2 3 " as $0 is not included in "$@" ($0 is 1, $1 is 2, $2 is 3). It's very easy to just always give the shell name itself manually as $0 instead of trying to ingest "$0" into your logic.
Of course, you could `find . -maxdepth 1 -type f -name '*.sh' -print0 | xargs -r0 ...` instead, depending on what you're up to, that may be the easiest. It's definitely the simplest -- as long as your xargs has -0 support.