The paching is upgrade Oracle binaries - sqlplus, svrmgrl, tnslsnr, etc. including the kernel for the Server + step for the db upgrade by inself + ODBC + JDBC drivers, etc.
In Oracle client you still have ODBC, JDBC, SQL*Plus, Net8, etc. binaries/drives, so go ahead and apply the patch. It will upgrade whatever binaries are in the ORACLE_HOME you select from OUI. And skip the steps for db upgrade, edit the pfile, etc. - since you don't have them anyway.
I did it on Solaris 7 / Oracle 8.1.7 Client. SQL*Plus still shows 220.127.116.11.0 but sure drivers and other files got upgraded.