I was playing around the other day making a cyborg character of my own and mentioned on Discord that by the time I paid for all the prosthetics I did not have enough for more than a survival knife and it was suggested to me that if I ever played it I should ask my DM to waive the cost of the prosthetic arm and leg as they were merely cosmetic. I think that is probably the sensible approach in any case. Under the RAW I think you would have to pay for the arm period (heck, under RAW I am not sure you could even combine a prosthetic arm with the custom rig because I think the custom rig "takes up" the space you install it, except when you install it with a datajack). So yes, you can waive the cost of the prosthetic.
This way that character, by the way, though the name was a bit of a placeholder,

. The concept was that most of her right side had been ruined in an accident or disaster.
[sblock=Half-n-Half]
Half-N-Half
Female Human Cyberborn Augmented Mechanic 1
Alignment: Chaotic Neutral
Resolve: 2
Exp: 0
Appearance:
Statistics
Str: 12 (+0) 2
Dex: 16 (+0) 4
Con: 10 (+0)
Int: 14 (+0) 3
Wis: 10 (+0)
Cha: 11 (+0) 1
Stamina: 7
Hit Points: 10
KAC: 13
EAC: 13
Initiative: +3
BAB: +0
Speed: 30 ft.
Saves
Fort: +2
Reflex: +5
Will: +0
Feats
Human - Skill Synergy (Life Science and Acrobatics)
1 - Toughness
Exocortex - Skill Focus (Engineering)
Racial Abilities
+2 Dex
Medium humanoid with human subtype
Bonus Feat
Bonus Skill
Theme: Cyberborn
1 - +1 Computers, -5 DC to Engineering to identify cybernetics and Life Science to recall knowledge about cybernetics
Class Abilities:
Proficiencies - Lgt Armour, Basic melee, grenades, small arms, Hvy Armour and long arms*
Artificial Intelligence (Exocortex)
Bypass 1
Custom Rig
Skills
Acrobatics 1, +7
Athletics 1, +5
Computers 1, +7
Engineering 1, +7
Life Science 1, +6
Medicine 1, +6
Physical Science 1, +6
Languages: Common + 2
Augmentations
Custom Rig
Vocal Modulator, 125
Respiration Compounder, 250
Prosthetic Arm and Hand, 100
Prosthetic Leg and Foot, 100
Weapons
Survival Knife, +3 atk, 1d4+1 S, Analog, Operative, bulk L, 95
Armor
Equipment
Industrial Backpack, Bulk 1 (Str +2 to carrying capacity), 25
Shipsuit (Environmental Clothing; +1 vs Radiation and +2 to Zero-G movement), Bulk L, 40
Planetsuit (Environmental Clothing; +2 vs Cold and hot temperatures), Bulk L, 40
3 Everyday Clothing, Bulk 3L, 3
Hygiene Kit, Bulk 1, 3
Flashlight, Bulk L, 1
Canteen, Bulk L, 1
Datapad, Bulk L, 55
Standard Battery, Bulk 0, 60
Zipstick, Bulk 0, 10
Lighter, Bulk 0, 1
Trapsmith's Tools, Bulk L, 20
Gear Maintenance Kit Bulk L, 5
Total Bulk 2.1
Money 61
[/sblock]