Can I get Shadowmere if I've abolished The Dark Brotherhood?

Without Cheats

The simple answer to your question, without cheats, is no.

The game is specifically scripted to give you Shadowmere once you have completed the Dark Brotherhoods quest related to the horse.

With Cheats

With cheats, you can get Shadowmere however. First open up your console, and type:
help Shadowmere
It should come up with an "ID" for the NPC for Shadowmere, this is what you want to spawn in.

Then, type in:

player.placeatme 0009CCD <- Replace with the ID for Shadowmere, although I'm sure that is the ID.

Shadowmere will spawn in next to you, now select Shadowmere by clicking on him/her/it while the console menu is open. Now type in:

setownership

And Shadowmere should be yours.

Conclusion

I understand that you want to play the game legitimately, and I'm like that too. But if you really want Shadowmere, perhaps a good way to "roleplay" it would be to say to yourself that you found him/her/it while destroying the hideout and tamed him/her/it? Up to you.