Weapons in general are very personal. There's no real "one size fits all" option. That said, the trade-off for "covert", or ease of concealment is usually comfort. Almost all of the thumb daggers, push daggers etc , designed EXCLUSIVELY for concealment are usually uncomfortable during use because of how thin the steel is. During impact, if you're not spot on with your targeting, you will definitely hurt your hand. They're designed only as last ditch weapons to create space. They can be modified to feel better, but adding width to the grip, kills the whole concealment concept. My best advice is actually the la Griffe. Thin, flat, sharp, and the ergos are perfect for thrusting and slashing. I didn't recommend it, because the OP asked specifically about push daggers. The la Griffe will also fit inside a wallet or phone case.
Last but not least, usually removing scales will kill a knife design, but if you REALLY inspect the blades I recommended, you'll see that yue the pistol gripped profile of the ka bar ldk, and the deep finger grooves of the crkt minimalist keep them pretty safe options regardless of thickness. They'll just be less comfortable obviously. Depending on how large your phone case is, you could even do it with a cold steel mini tac. It's all about the design. ( Deep finger grooves/ guard). Let me know if you need any other info. I'm not an expert, but Ive been around.

Looking for my shadow...in the light.