I was thinking back to the Necromunda and came up with this. I'm not entirely happy with it so feed back welcome.

Underhive (Hive world )

Almost every hive in the Calixis sector has a dark lawless region known as the Underhive. It is the lowest levels of the hive below the feet of most of the workers. Over hundreds of years these lower levels have deteriorated, intend changes and collapses turn it into a dark warren of dangers.
To add to the natural hazards the underhive is a beacon for all the worst elements of the hive, mutants, criminals, heretics and other horrors have carved out a place for themselves down there. Even in the lawless underhive there are levels, the top levels are ruled by large gangs constantly warring for territory while lower levels are almost to dangerous or toxic for the normal gangers. Only the most desperate call these lower levels homes. True outcasts those too mutated hide their deformities, too diseased for others to tolerate or too insane and heretical to live with even outlaw gangers.

Playing an Underhiver PC.

The Underhiver will have grown up in a close knit gang fend for themselves with what they can steal or barter far from the eyes of the Imperium but under its very nose.
There is a number of reasons that a character could end up in the employ of an Inquisitor. The Inquisition often has to track through the Underhive to chase the enemies of the Imperium and the people that grow up down there are some of the most resourceful and loyal of any hivers. They will have grown up with constant danger and only there close relations to look too. Often the Underhiver will have joined Inquisition after his gang was destroyed, after he was cast out (sometimes for helping the authorities) or he agreed to join the Inquisition in return for help or amnesty for his brothers.

Creating Underhiver characters

Instead of 'Accustomed to crowds' and 'Caves of steel' they have the following traits:

Wild depths
Instead of the normal statistic changes for a hiver they use:

Statistic Roll
Weapon skill 2d10+20
Ballistic skill 2d10+20
Strength 2d10+20
Toughness 2d10+20
Agility 2d10+25
Intelligence 2d10+20
Perception 2d10+20
Willpower 2d10+20
Fellowship 2d10+15

So if the players stats have been rolled change the statistic total for Fellowship to be the new Agility score, the total for Toughness becomes the Fellowship stat and the total for agility becomes the Toughness stat.

In addition the character gains 1d5 insanity points.

Outlaw youth
The character begins play with the Secret tongue (Gutter) and gain Peer (Criminals).

Well I get the Stats change and the skills change, as well as gaining the insanity points. Personally I reckon thier strength would be 5 less then average and perhaps they have a 5+ toughness in return. (Given the nature of food sources?)

However what replaces the two charactistic traits you removed and balances the insanity point gain? (Most alternate upbrinings add an equal amount of charactisics they removed and insanity points are added usually at the cost of an additiaonl skill or power/talent.)

Just use the rules for Hive Volg. They seem to cover the whole lawless underhive pretty well.