Funny thing. When you go to the ccleaner actual web site it says it's for 32 or 64 bit as you said. However I use the portable one and nothing gets installed on the computer but still works great. When you download that it's in a zip. Unzip and it has an .exe for 32 and one for 64. I just use the 64 as my system is 64. Also put an icon on the desktop and just drag it to my dock(s) then get rid of the desktop icon. As long as you keep the exe file in the same folder it will always work, but guess you all know that already.

Actually this might be a 32 / 64 bit issue.

I seem to recall ObjectDock is a 32 bit process and unless ccleaner installed a 32 bit shell extension dll on a 64 bit system as well as the 64 bit one then the links may well not show up.

Because one isn't needed.

It is not like it is going to use more than 2GB memory and having a single exe reduces installer size and the risk of odd bugs showing up in 64 vs 32 bit.