No, not if the 93 has stock exhaust manifolds and cats, or a combination of exhaust manifolds (or headers) and cats (or test pipes) that end where the stock cats end on a 93. To make it work you would have to modify the existing cats and / or test pipes to end where they do on an 02+
Alternatively, you can modify the 02+ ARC to work on the 93.
Unless you also have plans to upgrade the exhaust manifolds and cats at the same time with compatible parts, it would be better to just find an ARC that is built for a 93 (which will get harder and harder now that they have gone kaput).
J