It isn't that bad to get a 6 weapon skill (bear in mind, I'm not talking a weapon skill group) and a specialization at character generation. It is only 7 skill points. Even if the character uses priority E in skills that still leaves 11 points. Could put 6 in Perception, and 5 in Negotiation for a hired killer. Or 5 in Survival for a hunter / militia / NRA member.

But it it is still too expensive, shift the weight to Agility.

Race: Elf
Qualities:
Exceptional Attribute (Agility) [14]
Restricted Gear [10]
Gear:
Muscle Replacement 4 (100000 ) - or if you are more concerned about Essence you can go with Muscle Toner 4 Bioware for 28K more.
Optional:
Vision Magnification

Then you have 12 Attribute, and with a 2 Skill (without specialization) you can get 15 dice with a Take Aim - and reduce range penalties by one category if you take Vision Magnification.

Of course, you could increase the skill to starting max, grab a specialization, add in Smartlink and get a pool of 23 with a Take Aim.

Would this character be playable? Depends on the table. For some, this build (with 23 pool) is the baseline of a starting character. For others, the player who brought this to the table would be ridiculed and shunned.

I can't say how well it would fit. Just that it is easily within the rules.