If your GM rules that spells with multiple damage types are eligible to have one of them replaced, you can replace any one of the choices, and choose the replacement.
Regardless of when you make the choice of which damage type you want for the spell, before you've made your choice you might be able to replace one of them (and then choose the replaced type).
If your GM rules that spells with multiple damage types are not eligible to have one of them replaced, it comes down to the GM's ruling on when the choice is made.
A spell with multiple damage types in a list that you choose from is a spell with multiple damage types before you cast it, but one damage type after you've chosen. Once you've made your choice and the spell has "a damage type," (rather than "damage types"; "a" is singular) it is definitely eligible to be replaced by Awakened Spellbook to replace that damage type.
However, does the choice happen too late? Importantly, the Awakened Spellbook feature can be used "when you cast" the spell—so if the choice is made after you cast the spell (and you're reliant on it only having one damage type to be eligible), it is too late to replace its damage type. So, is the choice made before or after you cast the spell?
The exact timing of that choice has not been clarified in the rulebooks or in Sage Advice, so your GM would need to make a ruling. The exact timing of other choices made regarding spellcasting could be useful in making this ruling:
- According to Sage Advice Compendium #SA153, the targets of spells are chosen after the casting. For example, Scorching Ray's second target is chosen after the first target is known to have been hit (or missed).