Cover a baking tray with parchment and melt the white chocolate in a microwave-safe bowl using 30-second intervals. Continue until the melts become smooth with no solid pieces remaining.
Stir the coconut oil into the melted chocolate, using additional brief microwave bursts if needed to melt it completely. The combined coating should flow freely rather than fall from the spoon in thick blobs.
Pour some coating into a cone, rotate it to reach the interior, and use a straw or skewer to spread a thin layer before shaking out the excess. Check that the coating reaches the narrow tip without leaving bare patches.
Rest the coated cone on the prepared tray and treat the remaining cones the same way while the inner layers set. The interiors should look evenly coated rather than pooled with chocolate.
Remove the Oreo cream centers, pulse the cookies into coarse breadcrumbs, and transfer the crumbs to a bowl. Stop while distinct little cookie pieces remain.
Process the freeze-dried strawberries separately to a breadcrumb texture, then wait a few minutes before opening the lid and mixing them with the cookie crumbs. The finished mixture should have an even scattering of pink berry pieces throughout.
Arrange the cones beside separate plates of melted coating and strawberry crumbs, with the tray nearby. Keep everything within reach so the chocolate stays wet during coating.
Roll approximately the upper third of a cone through the melted chocolate, shake away the excess, and immediately roll it through the crumbs. The strawberry-cookie pieces should cling to the wet coating without sliding off.
Return the finished cone to the tray and repeat the dipping process with the remaining cones. Leave the shells undisturbed until the outer coating has set.