Castle Rock is at high-ish elevation and it'll be snowier there than at the lake level traffic cams. There is a possibility that the south facing rock is melted out and dry, but it's also very likely that the approach trail will still be snowy.
The recent satellite imagery (Sentinel-2 satellite, 08-April imagery) seems to confirm this. Though a lot could change between now and next week - warm temps and things are melting fast. Though I suspect that the woods behind Castle Rock (on the Castle Rock approach) will stay snowy for a little while longer.
If you're OK with driving a bit farther for a completely snow-free outing, the south facing walls at Woodfords are a good option. Pie Shop should be fairly melted out by next week also.
If you also like bouldering, there is a lot of good bouldering out there that should be dry next week. The Zephyrs are a good option for early spring, and are close to Heavenly (refer to the Tahoe Bouldering East Shore book).
Caveat: this is based on general area familiarity and recent satellite imagery, but is not a current in-person conditions report.