This is gonna set some people off, but the simple truth is that Hiko would have lost to Shishio.
First, Hiko's defense is not impenetrable. Even before learning the succession technique, Kenshin was able to land a hit on Hiko when his focus and motivation were at 100%. That means Shishio would have likewise been able to hand hits on Hiko.
Meanwhile, Hiko's capacity to take damage is no better than anyone else's. Yes his muscle mass gives him some protection, but it didn't protect him from the Amakakeru Ryu no Hirameki. And consider getting hit by that technique knocked him out for a full day, whereas Shishio could withstand the full force of the stronger version of the technique and keep fighting, and even Aoshi could maintain consciousness. That suggests one Guren Kaina would have knocked him out, and even Homura Dama would have whittled away his fighting strength.
All of which is to say, his build, technique, and blade give him incremental advantages over Kenshin but not so much that motivation and fighting spirit wouldn't factor in. And on those counts, Kenshin is leaps and bounds ahead, being more invested at an ideological level (caring more about what happens to the government) and a personal level (redeeming his own legacy as hitokiri), contrasted to Hiko's personality ("twisted, brusque and misanthropic") and politics (the Hiten sword must maintain its independency from factions)
All of this is set up within the narrative itself, which is why Kenshin didn't bother asking his master to help him out. Of course, protecting the weak from roving bandits is right within his wheelhouse, which is why he is willing to protect the Aoya.