Can I use classic skis for skate skiing?

No. Classic skis and skate skis have fundamentally different designs. Classic skis have a grip zone (waxable or waxless) and a camber pocket optimized for the diagonal stride. Skate skis have no grip zone, a stiffer camber profile optimized for the skating push-off, and are typically shorter with more sidecut. Using classic skis for skating will result in poor performance and potential damage to the grip zone. If you want to do both techniques, you need two pairs of skis or consider a combi ski (a compromise option that performs adequately at both but excels at neither).