This is actually the key question to parsing this ability: "can I change Stoneskin to give me fire resistance*?"
Lets look at the text: "When you cast a wizard spell with a spell slot, you can temporarily replace its damage type...". The answer is no. Stoneskin does not have a damage type. There is no ambiguous word "appears" there.
The next part of the sentence is what is causing the confusion: "with a type that appears in another spell in your spellbook". This indicates that if you can replace A with B you can also replace B with A. If I know Alter Self and Acid Arrow I can create acid damage claws or I can shoot slashing damage arrows. It's either both or neither.
What the word "appears" does do is let you select any damage type when the spell has a choice. If use absorb elements to absorb cold damage, I can use this ability to replace the cold damage I would do back with force damage from my magic missile. Very useful, since creatures are often resistant to their own damage.
*note that 5e does not distinguish between magical and non-magical fire damage. Fire damage is fire damage. It also impossible for a spell to do non-magical damage of any type. Spells are, by definition, magic. See the sage advice on Hunter's Mark.
All great points. Thank you!
Now, about the bolded part - I'd say we have some RAW evidence that there
is a distinction between magical fire and nonmagical fire and, therefore, implicitly there
is magical fire damage and nonmagical fire damage (note, I'm not defending using
Stoneskin with Awakened Spellbook, I'm just curious about exploring this assertion):
DMG p61: "Wind quickly extinguishes nonmagical open flames such as torches and campfires."
DMG p219: "While attuned to the artifact, nonmagical flames are extinguished within 30 feet of you."
PHB p197: "For example, if a creature has resistance to fire damage as well as resistance to all nonmagical damage, the damage of a nonmagical fire is reduced by half against the creature, not reduced by three-quarters."
MM p8: "Particular creatures are even resistant or immune to damage from nonmagical attacks (a magical attack is an attack delivered by a spell, a magic item, or another magical source)."
EGW p151: "Nonmagical fire can't burn here."
I believe there are more such examples in some adventures, but I think the point is sufficiently made.
Of course, the point is a bit moot (for now) as no current WotC-published monster has resistance or immunity to general
nonmagical damage or to specific
nonmagical damage that is not piercing, slashing, bludgeoning. Then again, that doesn't prevent a DM from homebrewing a monster that is resistant or immune to nonmagical fire damage, for example.
Then
then again, this doesn't have much to do with the OP other than being loosely related to spells that a wizard may or may not be able to cast - so sorry about that!