It looks like the few distros that used to offer libressl as the default no longer do so. Even the last die hard ultimate customization Gentoo Linux is stopping support for libressl due to time and effort:
LibreSSL languishes on Linux (posted on 2022, 01, 04) (https://lwn.net/Articles/841664/)
But if you still want to try then:
The packages in question would have to be compiled to use libressl. Then one would have to update and upgrade those packages manually themselves afterwards to keep stuff current. Some software projects will need patching in order to compile with libressl. Then those libressl linked packages will use the libressl library instead of openssl. The packages in question may need to be configured afterwards depending on the project.
Using it in a few packages would be not too much but it would take some effort if you want to completely replace openssl. There are quite a few packages that use a "SSL" library. In the end your setup would be no longer Artix but a derivative of it. Any issues you may have would have little to no help because no else has your configuration. This is kind of like making your own distro in the end.
TL; DR You can't, and no .
This also applies to all replacements of core libraries linked by many executables (i.e. no using musl over glibc, no using libc++ over libstdc++...). And performing similar replacements is impossible in every binary distro, not just on Artix.