I am not a big fan of patching. Personally I remove all Magento files from their directories then upload the new version (using a shell script). All the files installed over the years like modules or themes are still there. For database I make a comparison between fresh installed versions. One way is creating or removing the columns/tables into the database, the other way is installing again Magento just changing /app/etc/local.xml file name. I prefer the first one.
If you do not change the database structure to version 126.96.36.199 you will get some errors or you cannot load admin area. If anyone is interested in some comparisons for Magento directories and databases between Magento CE 188.8.131.52 and 184.108.40.206 just download the file from here:
Magento Comparison: versions 220.127.116.11 - 18.104.22.168
There are two html files with very nice visual results.
I updated 4 stores today using my method instead of patching. All are running without any issues.