Though you don't want to make a full backup, you might still wish to take a look at Full Backup of non-rooted devices to get an idea what is possible. That page also mentions some helpers for your issue:
- Simple Backup runs from your computer and, as the screenshots indicate, can also be used to backup a single app (so you could use it for each app you want to backup)
- Helium Backup (formerly known as Carbon Backup) is an app you can install to your device. Select the apps you want to backup, start the process – and it creates a separate backup file for each app. Which means, you can restore them separately/selectively.
- It's also possible to do this via the command-line, which might be a little non-intuitive.
- Not on that page, but making the latter a little more easy: Adebar is a tool I wrote (and am still on it – it's far from being complete yet). It creates you scripts for backup/restore (where you simply can comment-out/remove those apps you don't wish to take care for), plus more. Possible drawback: Adebar is written for Bash, so you will need an OS that has this (Linux, and possibly also Mac should do).
There's one thing all those have in common: they require ADB-tools to be available. For that part, you can take a look at Is there a minimal installation of ADB? to avoid installing too much with too much hassle ;)
If you find another app promising easy backups without requiring root or ADB, be aware it might leave your apps' data out! To my knowledge, before Android 4.0 only root-apps were able to backup app data, and with 4.0 only the option via ADB became available. Make sure to read the description of such an app very carefully.
To pick an example (experience of the OP, sadly): There's an app called App Backup & Restore. On a quick view it sounds like a perfect match. But looking deeper into the description you will find:
App Backup cannot backup data or settings of apps for you, but it only backup the apk files.
Which means: It only cares for the apps themselves (which you always could re-install from their respective sources anyway – with the added work of looking them all up separately, and maybe some of them disappeared, or are no longer available in a specific version you might want for some reason – so this app still has a good reason to exist), but doesn't cover their data.