If you have customised php files (over-rides) then much will depend on how disciplined you have been in managing your cutomisations. By this, I mean that you have observed the procedures for creating customised files, and that you have placed them in the appropriate over-rides folders.
When you UPGRADE, the process involves over-writing existing php files - all excepting those located in over-rides directories.
The problem is that your custom php files will remain version 1.3.7.
What you need to do FIRST, is unzip a version of 1.3.8.a on your local drive.
Then, FTP back to your local drive, all the 1.3.7 files you have customised - keeping the structure of the directory tree intact. It is advisable to FTP your ENTIRE SITE back to your hard drive.
If you do this, you will have a copy of your 1.3.7 site (all the php files in their correct folders) on your hard drive, AND you will have a copy of the 1.3.8a files in their directories.
Now, you have to COMPARE the 1.3.7 files with their corresponding 1.3.8 files.
The tool to do this is called WINMERGE, and it can be downloaded free off the internet.
WINMERGE will quickly compare all your files in your hard drive's 1.3.7 directory with the files in your 1.3.8 directory.
It will list all files that are not identical.
Now... if there are CUSTOM 1.3.7 files that you created, you will use WINMERGE to make adjustments.
WINMERGE will show two side-by-side panes of the similarly-named files. For example, in the left pane you will call up the 1.3.7 "tpl_product_information.php" and in the right pane call up the 1.3.8a "tpl_product_information.php".
WINMERGE highlights all the lines that are different.
You now need to put your customisations into the 1.3.8a version - making sure you don't erase important lines of code.
Now that you have a record of all customised file changes on your local drive (you know what 1.3.8a files need adjusting) you start the upgrade. Use a fresh version of 1.3.8a - not any files you've changed in winmerge!)
FOLLOW THE UPGRADE PROCEDURE!
Now, on your local drive, (and using winmerge again) adjust any 1.3.8a files to suit your original 1.3.7 customisations
When the upgrade is complete you can start FTP-ing your customised 1.3.8a files into their over-rides directories.
This process sounds tedious, but it isn't. It takes a bit of time (a couple of hours) but will certainly be faster and better that what you are proposing to do.
The key to this is following the over-rides procedure when you make changes to core code files.
If you maintain strict discipline, you will find upgrading easy, logical and fast.
Also, you will know that your 1.3.8a site retains its integrity - and that's perhaps the most important thing to consider.
