A push-up with your hips high in an upside-down V — shifts the work onto your shoulders. The closest thing to a shoulder press with no kit.
Every move in Core Buddy has a video like this one — and it builds the whole session for you, timer and all. Free to download.
The pike push-up with your hands on something raised and steady. Same shoulder work, less of your weight to press. Work with this version for as long as you like — when the full one feels within reach, give it a go.