I found the code to make wool blocks break faster with shears in the ItemShears class:
 

public float getDestroySpeed(ItemStack stack, IBlockState state) {
	Block block = state.getBlock();
	
	if (block != Blocks.WEB && state.getMaterial() != Material.LEAVES) {
		return block == Blocks.WOOL ? 5.0F : super.getDestroySpeed(stack, state);
	} else {
		return 15.0F;
	}
}

It checks specifically against wool, and the superclass method in Item just returns a constant. (As far as I'm aware, I can't override this item method of shears from my mod block class, since the shears handle the speed, not the block.)

Is there a way to get a custom block to break faster with shears, like wool?

What kind of block is it? You can try to extend your custom block with wool block

You can override the vanilla shears item and change the getDestroySpeed method.

Just create a class that extends the minecraft shears class, set the registry name to "minecraft:shears" and register it.

But be aware that this will cause issues when another mod also overrides vanilla shears.

You can override Block#getPlayerRelativeBlockHardness(IBlockState state, EntityPlayer player, World worldIn, BlockPos pos), check if the item in player's main hand is shears and return a lower value.