Magento 1.9.2.4. updates the following files from 1.9.2.3:
- app/code/core/Mage/Adminhtml/Helper/Sales.php
- app/code/core/Mage/Core/Model/Config.php
- app/code/core/Mage/Sales/Model/Quote/Item.php
- lib/Varien/File/Uploader.php
Without knowing the exact files you mean by "custom files", if any of these files are overridden in the app/code/core or lib/ directory which is considered bad practice, you can copy these to app/code/local before upgrading.
e.g. "app/code/core/Mage/Adminhtml/Helper/Sales.php" would be copied to "app/code/local/Mage/Adminhtml/Helper/Sales.php".
See app/Mage.php and lib/Varien/Autoload.php files for how autoloading works in Magento.
You can also upgrade using shell providing you have shell access and you know how to use shell. I would also test this locally before applying on a live site.
You can download and apply the patch 7405 from www.magento.com/download for 1.9.2.3 to 1.9.2.4 by moving the patch file into your Magento root directory and then from the command line
- cd path/to/magento_root
- sh patch_file_name.sh
Then delete the the patch file name.