Having avoided spoilers for Skyward Sword for a long time, I won't get too much into its relation to The Minish Cap, but from what I know, my guess is that it rather certainly takes place before The Minish Cap considering how established Hyrule is in each game.
On that note, if you consider how established Hyrule is from game to game, there's little leeway for The Minish Cap to take place before Ocarina of Time. In The Minish Cap, we have a Hyrule that is well-established and has certainly been standing for a long time. At one point the game we enter the Royal Crypt where we meet the ghost of the deceased King Gustaf, a previous King of Hyrule who passed away ages ago. Obviously, the kingdom of Hyrule is at least as old as Gustaf's grave.
By contrast, however, the Hyrule of Ocarina of Time is still a new kingdom. The birth of that game's Link takes place during the Hyrulean Civil War (not the official name, but you can find it under that name on Zelda Wiki). This war results in the unification of the kingdom of Hyrule, making it a relatively new kingdom. We can still see the remains of the separate kingdoms of the different races during the child portion of the game where, although they are all unified through the royal family, the Gorons, Zoras, and especially Gerudos still keep up their borders rather effectively (which, for the Gerudos, persists through the adult portion of the game).
Saying the story that takes place in an age-old kingdom takes place before a story where that kingdom is new simply doesn't flow. The Minish Cap cannot take place before Ocarina of Time.
We can, perhaps, still find some plot/timeline significance with the hat. In Skyward Sword, Ocarina of Time, and Twilight Princess, we're provided an explanation as to why Link wears his tunic (which also applies to The Wind Waker, Phantom Hourglass, and Spirit Tracks on the other side of the timeline). In my own timeline theory, The Minish Cap takes place on the Child Timeline and precedes all the other 2D Zelda titles (going by graphics), all of which don't explain the fact that Link wears a tunic far beyond the suggestion that it becomes sort of standard among a certain persuasion of Hylian boys. I'm inclined to think it's supposed to be a uniform for the Knights of Hyrule, of which A Link to the Past's Link is the last at the time. We can't say for certain whether the uniform is derived from the previous heroes of Hyrule (in particular Twilight Princess's hero), but its logical that at this point, where the whole outfit begins to become standard, the touching little story of Link obtaining his hat begins the tradition of incorporating the hat to the uniform of the Knights of Hyrule, particularly among Link's line. Now, we could probably debate whether these Links in particular are actually blood-related, and otherwise we could speculate as to how the tradition of incorporating the hat is passed down, but Link obtaining the hat does work as an indication that The Minish Cap takes place first out of the 2D titles.
As for the Light Force, I'm not sure we can say it affects the timeline much. It's highly doubtful that it's the Triforce or any piece of it considering the nature of the Light Force, where Vaati drains a significant portion out of Zelda who later pours her remaining portion out upon Hyrule. We know that the Triforce or any piece of it functions as a solid object, making the draining and pouring questionable. We never see the physical form of the Light Force where any other game would show the physical form of the Triforce. Our only indication of it having a shape at all is the drawing of it in the room behind the Elemental Sanctuary. The most likely reason it there bears any resemblance to the Triforce is because the developers wanted to reflect that motif, though in terms of plot I can't see the Light Force being logically considered any portion of the Triforce.
