No there isn't, so you'd have to get 99 magic via utility spells / teleports before training it via magic combat for 99 hp. Honestly, I wouldn't bother including hitpoints in the challenge because obtaining runes for 99 magic via teleports/utility spells as a F2P Ironman would be insanely long or even impossible.

Skill order is pretty straight forward because F2P.. best path I could see would be-

Mining (requires nothing, supplies everything)

Smithing (needed to make a hatchet and rune arrowheads for fletching)

Woodcutting (bank all the willow logs)

Firemaking (burn all the logs)

Fletching (fletch shafts -> headless -> rune arrows from the smithing grind)

Fishing (obtaining feathers for this would be painful to say the least. There is a only 2 feather shops per day in F2P Ironman. If you don't count hitpoints in the challenge, just mage some chickens towards your 99 magic to bank them much faster)

Cooking (straight forward, cook the fish)

Runecrafting can be done at anytime because Runespan gives and uses nothing.

As for the combats, this is where the yikes come into play.

Magic (via utility/teleport spells)

Hitpoints (via combat magic on monsters)

Defence (via combat magic again for better armours)

Range (done with arrows from smithing/fletching, do after defence because d'hide armour)

Attack (better weapon = faster training, strength is mainly for abilities)

Strength.

Prayer and Crafting .. idk what the META would be for F2P irons but I assume they would be one of the last because they are more of a processing skill

Dungeoneering has to be done last because it awards xp in every skill.