The good news is that you just need to update the one hotfix jar. While it is discussed in the technote for the hotfix, the note about this update is sadly (currently) at the BOTTOM of the technote. I'll repeat what it says here, to give it some more visibility:
Note - Updated on March 29, 2012
Following bug is reported for ColdFusion 801 against this security bulletin hotfix.
java.lang.NoSuchMethodError Exception is thrown while using cffile upload.
We have updated the hotfix files of ColdFusion 801 to include the fix for the above issue. Users who have already applied the hotfix for ColdFusion 801 can just update the hotfix jar.
I'm pretty sure this is fixing what some found to be a reliance in the hotfix on your having applied one of the specific Cumulative hotfixes, but if someone had not, or if they inadvertently removed the CHF during the process of adding this single one, things would break. I'll note that the HF technote above does say very specifically what jars to remove, when applying the hotfix. Some people in haste instead delete all the hf and chf jars, or delete chf hars when it says to remove only hf jars. They so look similar in name.
I cover this issue of being careful about applying hotfixes (there are other mistakes you can easily make) in another blog entry I did, CF911: Are you finding CF (or CF Admin) busted after applying a hotfix? Three possible reasons.
And before someone chimes in to lament, "this is what's so wrong with the CF hotfix process, that mistakes can be easily made", I cover that too. The short answer is that Adobe is addressing this in CF10, and may even offer something to help us later for CF 8 and 9. We shall see.