I have done a couple of these now, one of them on a very large site. I would definitely upgrade v4 incrementally to each minor revision because the upgrade process was not as reliable as it is now and there is potentially breaking changes as well as a number of files to remove. Read ahead about the Version specific upgrades found on the Our Umbraco site.
Luckily for you, there are Nuget packages all the way back to the version you are starting from so I would take advantage of that and upgrade the package at each step and commit your changes to your source code repository and tag them before moving on to the next. It helps when you come to repeat the process on your production site.
So, my first attempted upgrade path would probably be as follows:
4.8.1 > 4.9.1 > 4.10.1.1 > 4.11.10 > 6.2.6 > 7.5.x
One of the biggest gotchas I found was reading the release notes and making sure you REMOVE all of the files that are no longer required and detailed in the release notes.
Compared to how it used to be there is now a lot more information around to help you if and when you get stuck.