Not on literally her first try, no.
She can pry out a bit of the strange mana-flavoring-structure, presumably Earth-affinity mana, from its underlying material; she can hold the resulting Earth-affinity mana for as long as she cares to; but once she takes the affinity-mana out of an underlying material she can't put it back, just like she couldn't have done that in Golarion if she was trying to burn magic into something without any spellsilver to help.
The entire structure of the blade looks like... actually, it looks like somebody used smithing tools to lay down a pattern of affinity material, rather than burning a magical pattern into the material using outside power - as you might expect, given that there's no spellsilver involved. You can literally see the outlines of the magic physically in a pattern of the blade alloy.
Carissa could potentially refine that pattern some by selective ablation, or maybe by pinching the affinity-magic that runs through a material to be a narrower more intense band in places; without her having to reforge this whole blade, or her getting a few dozen pounds of spellsilver and learning how to produce the flavored mana.
Before then, it might help if Carissa had any idea of what it looked like to actually activate this blade, because right now, based on any laws of magic she knows, this spell-pattern cannot possibly work; she can intuitively see how it's trying to yell "SHARP" at the metal, and she can definitely see how it would leak mana while yelling that, but not how that yelling actually... helps.