I am developing a game that had minigames that are based on skill that do not involve any luck.
The first minigame I implemented was snake and I cant think of any other games I dont wanna spend a lot of time building out the minigames and I would like the time that is required by the minigames to be under 10mins
Look at old Atari 2600 games. There is a wealth of ideas to draw from.
Games from the golden age of arcade are generally designed to be short too.
What are you making them for? Personal practise, or for a larger project?
You can go back in time to arcade as @Ryiah suggested, another good place to look is the old flash minigames that many of us used to play at school. Armor games, miniclip etc etc, but you may need to use something like waybackmachine to see the truly old listings.
A lot of those games were made by a single person, and got an amount of hits that would be considered a success by todays standards. Most were before the days of monetization too so they tend to be free of F2P mechanics. All in all I think that makes them great candidates for remaking, either as practice or as part of a larger project 
Look at party games
If you do this, raving rabbids early games is a good reference product!
Thank you all for the great suggestions it’s for a larger project, looking at old Atari games I was thinking about adding “Dodger” into the game my issue right now is how fun will these actually be in today’s world?
You just made me remember a big douche move they made, I was about to register a user on armor games, every time he told me the captcha is wrong, I though I was high and didn’t read it properly… for the first time… second time… third time… okay, something else is going on here…
turns out (and I called my sober brother over to confirm it! and tried several times with multiple accounts, so i’m a 100% on this) if you tick off the receive newsletter it doesn’t let you register!
The goddamn bastards!
at that very instant I vowed never to go to their website again I’ve kept my flash gaming to newgrounds and kongregate.
just poped over there for the first time in years, the sites looks totally different and the registration is also different with no captcha.
but I swear to you this was true some years back, something like 5-6 years ago i think…
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