You should probably remove excess stain before it turns tacky. Remember, stains seep into the wood, they provide no protection being on the surface.

You want the surface absolutely dry before clear coating. If the drain doesn’t dry off, I would suggest applying some solvent- whatever is recommended for thinning by the product to remove the tacky stuff if you were trying to recover it.

For sanding complex shapes, you might be able to get a tumbler or vibration tank. Sand blasting is very aggressive, even using finer grits; and plastic is very soft. I’ve had good luck with spongey dremel wheels, if one’s in a hurry, or, using foam sanding pads.