Copying save files to new PC

[Jahshxjjfkk]

Hello!
So I've been doing some research while trying to find the best way to transfer my saves from my current laptop, to a new laptop.
My issue is this though: my current laptop is so slow that backing up my entire Steam folder would take days, if not weeks. (Writing to external Micro SD card, it's painful. My USB ports are borked and unreliable, so external HDDs are out too... :/ )

So of course I'd like to just get the save files, without any extra fluff, but how can I be sure I am getting ALL my save files? I'd hate to notice I lost a save file several weeks down the road...
I'm a little hesitant when it comes to using third party software, partly because my current laptop basically has no more room for anything, and partly because I wouldn't want to risk getting banned for any reason. (Using third party software to handle Steam data seems like a grey area.)

So TL;DR: best way to make a copy of ALL my saves, but ONLY my saves?

Thanks in advance! :)

[Snapjak]

https://www.gamesave-manager.com/

Probably the easiest way beyond relying on the cloud.

[xarvn]

1. Games supporting Steam Cloud will have automatically saved game progress on the Cloud (Steam servers). This is assuming you have enabled Steam Cloud. For Steam Cloud supported games, you can continue play on the new machine where you left off on the old laptop. You do not need to copy the save files over. See: https://support.steampowered.com/kb_article.php?ref=6736-QEIG-8941.
2. Not all games support Steam Cloud.
3. Games that do not support Steam Cloud do not save their game progress in the Steam folder. Hence copying the Steam folder over to the new computer does not transfer game progress for games that don't support Steam Cloud.
4. For games that don't support Steam Cloud, the save location is not standardized but usually they can be found in the AppData folder (see this) or in the Documents folder. There are some games, however, that save progress in some odd places. You will need to find where the games are saved for each of these taking note of the exact location so as to duplicate it in the new machine.
5. As you can guess, the process can be tedious especially if you have a large number of Steam games installed.
6. You can get around the USB problem by sharing files over a network (assuming you have a working ethernet jack or good WiFi capability). You can also remove the hard drive from the old Laptop and place it in a USB enclosure or dock. The new laptop should be able to read this drive provided your old machine did not use BitLocker or some other form of encryption.
7. Once you have implemented the above step, you can move your Steam games over to your new laptop. This will save you from having to re-download all your games and should not take very much time. See "How do I move my existing Steam Installation?" on this page.

Sorry for the long post.