Minecraft Java Edition – Blocks Requiring Silk Touch Enchantment

No, you still need a pickaxe for ores.

From the wiki entry on silk touch (emphasis mine):

Allows the collection of normally unobtainable blocks such as Ores , Grass , Mycelium and Huge Mushrooms . A pickaxe must be used for stone-based blocks (ores), while any tool can harvest grass, mycelium, huge mushrooms...

It is not possible to do that in vanilla Minecraft. Minecraft doesn't care what type of item it is, and will throw it all the same. It wouldn't be too difficult creating a mod which only lets you drop blocks, not tools, but you would need to contact a modder for this feature; as far as I know there are no existing mods with this capability.

I have run into this same problem, and have avoided the issue by going into the settings and changing the "drop item" key to something like G or P, making it much more difficult to hit the key by accident.