I want to be able to offer my DM suggestions about how this can work mechanically. I want to use the Broken One monk substitution levels from Champions of Valor 36-7 but use Tome of Battle's swordsage instead of monk. It seems that exchanging the swordsage class feature detect magic for the Broken One class feature locate creature at level 7 is reasonable, but what would be a fair house rule for the swordsage to acquire also the Broken One class features at levels 3 and 6 when at those levels the swordsage gains no special class features?
The fact that, lore-wise, a swordsage could be a member of the broken ones does not imply he could take a variant tought for a specific class.
What you need to acknowledge is that monks between the Broken Ones take the Broken One variant and this does not bar vanilla swordsages to be Broken One members.
If you wanted to get a swordsage variant for Broken One swordsage members, you should ask your DM for one. It's not automatic the benefits would be the same as the monk variant, just as there are different prestige classes aimed at differnt classes for memebers of other D&D orders (e.g. Nightsong Enforcer/Infiltrator).