Can I sieve pre-mixed concrete for thin applications?
Aggregate gives concrete much of its strength. Stone is much stronger than common cement mixes, and the pebbles create interior reinforcement that's critical to performance. The gravel also reduces cost and water consumption, but that's not relevant here.
The problem with your plan is that standard concrete isn't designed to be structurally sound in such thin applications. It will be very brittle and prone to shattering.
Products that are designed for thin applications tend to have additives, such as vinyl or latex, which make them much more flexible and robust in thin applications. They're the right thing for the job. They'll also be much easier to work as they don't tear as readily when troweling.