As you know, you can install 32-bit Oracle on 64-bit platform.So far so good.The main question is that how to apply CPU patch for this specific combination.
Regarding to metalink patch link, you only require to choose OS platform. (for example :HP-UX 64bit or HP-UX 32bit).
However, I figured out that Oracle32-bit can not be patched up on 64-bit OS if CPU patch is for 64-bit platform. As practical example, I tried to apply Oct2006 CPU patch to 32-bit Oracle home on 64-bit HP box.CPU Patch for 64-bit HP did not work (Many errors : Could not find $ORACLE_HOME/lib64) while CPU Patch for 32-bit HP worked properly !
Therefore, In the selection of proper CPU patch, 32-bit or 64-bit of Oracle home should be considered.(Do not fool with platform selection box in metalink)