a song of ice and fire - Is wildfire magical or chemical?

I came to think of it from interesting discussion at one of my answers regarding wildfire.

My understanding was that Wildfire is not magical because nothing suggests that it was. Granted that Order of Pyromancers keeps calling the manufacturing process a "spell" but they call everything a spell and hint at their own magical prowess as noted by Tyrion. The guild of Alchemists is not named so without a reason. If wildfire were magical, then that art should have been lost with death of the last dragon in Aegon III's reign as magic went begun to go out of the world then apparently. Some quotes from ACOK:

The substance was the pyromancers’ own term for wildfire. They called each other wisdom as well, which Tyrion found almost as annoying as their custom of hinting at the vast secret stores of knowledge that they wanted him to think they possessed. Once theirs had been a powerful guild, but in recent centuries the maesters of the Citadel had supplanted the alchemists almost everywhere. Now only a few of the older order remained, and they no longer even pretended to transmute metals...

Again from ACOK about "spell" on apparently fire-sensing ceilings:

By spell Tyrion imagined Hallyne meant clever trick. He thought he would like to inspect one of these false-ceilinged cells to see how it worked, but this was not the time. Perhaps when the war was won.

But counter argument is strong as well. Reforging Valyrian steel swords was still in practice after death of dragons which is also supposedly carried out with spells. Also existence of dragons seems to have improved quality of all fire-related "magic" spells. Admittedly it makes no sense that dragons should act as a catalyst in production of wildfire if it was not magic.

So the question is, Is wildfire really magical? Or the spells are simple chemical manufacturing processes for which dragons might play a role of catalyst?

Or can we say that while the procedure required to manufacture wildfire might involve magic but the end product remains chemical?

It might be opinion-based at this point since we do not know it for a fact right now but I'd like to see arguments based on canon sources which can help in determining the nature of wildfire.

Answer

Assumption: If wildfire were magical, then that art should have been lost with death of the last dragon in Aegon III's reign as magic went out of the world then apparently.

I disagree with this assumption. Magic in ASOIAF may have varying forms. White walkers were white walking way before dragons were hatched. Faceless men probably have their own form of magic. Children of the forest had their magic. Three eyed raven was watching over Bran long before the dragons. Warging was common beyond the wall. Albeit weak, warlocks of the Qarth had some magic of theirs as well, or they claim they have some magic.

The magic that disappeared or declined seem to be related to fire. Alchemists guild and Valyrian steel forgers suffered from this decline. Art of dragonglass candle burning was also lost.

So the question is, Is wildfire really magical?

My answer is yes, it is magical. Your only evidence against it is Tyrion's skepticism. Tyrion is a smart man, hence he is always skeptic. He was also skeptic of white walkers and giants, but we already know that his skepticism was pointless.

Hallyne the pyromancer and Tyrion had a talk about this.

Tyrion was growing impatient. Ser Jacelyn Bywater was likely here by now and Ironhand misliked waiting. "Yes, you have secret spells, how splendid, what of them" "They, hmmm, seem to be working better than they were." Hallyne smiled weakly. "You don't suppose there are any dragons about, do you?"

So, producing wildfire requires spells and art of wildfire did not die away with the dragons. Wildfire was, in fact the true power of Targaryens.

Or can we say that while the procedure required to manufacture wildfire might involve magic but the end product remains chemical?

I think this part of your question is impossible to answer. We know magic is involved. Is it possible to produce wildfire without magic? The word "spell" points to it. I claim a substance is magical if magic is involved in the production. However, in order to fully answer this question, we need to define chemistry, alchemy and magic in ASOIAF world. I hardly think we can precisely define them, so this part of question is more opinion-based.