Toys that kids can play with in general are not Mukza but should not be used by adults unless they need to move the toys for the sake of the kids (Sh"t Iggerot Moshe 5:22:10, Sh"t Beer Moshe 6:24, Sh"t Yabia Omer 7:39 thanks chacham Nissan from Halachapedia)
There are 3 potential malachos to be aware of: building by making an ohel tefach - a roof with a 3.54 inches width and length, knotting and untying.
1. בונה - Building an oheil (canopy) or rebuilding if it breaks
The Shulchan oruch orach chaim 301,40 says:
כובע שהוא מתפשט להלן מראשו טפח אסור להניחו בראשו אפילו בבית משום אהל a hat with a rim that has a tefach one must not wear because he is making a Ohel (i.e a canopy which is a form of building under the Melacha of Binian). But the Mishna Berura explains:
ודוקא כשהיה השפה שהוציאה קשה ביותר ואינו נכפף אז חשוב כמו אהל ואי לא"ה הרי הוא כגלימא בעלמא - as long as the 1 tefach (handbreath) rim is not firm and it bends in and out of shape it can be worn on shabbos.
So too here the parachute is not firm even though it is larger surface than a square handbreath there is no issue of ohel. But one shouldn't fix the parachute man if it breaks as we Pasken one should not build with Keilim in a permanent manner see Shulchan Aruch 314,1 and Mishna Brura.
This is also not applicable even if the parachute would get tangled so tight that it couldn't be untied as this is a Dovor she-eino miskavein (a melacha that is not intentional result which won't necessarily happen). The gemora in Eiruvin 100b deals with a similar issue and concludes that one may walk on grass with or without shoes; on wet short grass and dry; tall grass and short. The reason it is permitted is because the halacha is in accordance with R’ Shimon who holds that a דבר שאין מתכוין on Shabbos is permitted . The poskim add that this is on condition that:
1.It was not intended, over here you don't intend for to make the knot
2.It won't necessarily knot itself(לאו פסיק רישא)
So parachutes are permissible to be thrown by kids for pleasure as there is no intention to knot and it might not knot itself.
- מתיר- untying
The Shulchan Aruch and Rema@s explanation Orach Chaim 317,1 say:
דכל קשר של קיימא אפילו של הדיוט חייבין עליו וכן לענין התרתו דינו כמו לענין קשירתו - Any permanent knot one makes would be liable even a novices knot, and so too with regard to untying.
But if it is loose enough that one would normally untie it and carry on playing with the parachute, you can untie it.
וקשר שאינו של קיימא ואינו מעשה אומן מותר לקשרו לכתחלה:
הגה: וכן לענין התרתו דינו כמו לענין קשירתו (טור - A nonpermanent knot and it is not an expert knot one can tie (e.g a tie) and so too with regards to untying.
So if it gets entangled in a way that one wouldn't untangle it because it is too tight and therefore a permanent knot then one should not untangle it rather leave it.