"Vanilla Plus Spawners" datapack helps you craft spawn eggs and acquire spawners without making it too overpowered.
!Crafting recipe for skeleton spawn egg.
Diamond block surrounded by skeleton skulls.
!Crafting recipe for zombie spawn egg.
Diamond block surrounded by zombie heads.
!Crafting recipe for spawner.
From top left to bottom right :
For obtaining skeleton skulls and zombie heads, you can either kill zombies and skeletons via a charged creeper explosion, or you can use other mods and datapacks (like VanillaTweaks' More Mob Heads datapack.)
After obtaining the spawner, you will need either a zombie or a skeleton spawn egg to activate it. Just right click on the spawner while holding the spawn egg in your hand. (You can also do this while sneaking.)
Be careful not to waste your spawn eggs by right clicking somewhere other than a spawner!
To be able to have a proper spawner from scratch, you will need:

Adding a way to obtain zombie and skeleton spawners to the game without being too overpowered.