No worries,
I just did that exactly on a site. I went from 1.3.0.1 to 1.3.7 and it went well. I did do some custom coding and overwrites, and I was finished in one hour total.
What I did was put it in a sandbox first, make an sql backup of old site, added that to the new sandbox site, and then traced down the custom overwrites I did in my original folder.



