Depends what breed but if you were solitus you could get.....
Maxed Abilities, Maxed shotgun, Maxed fling gets you 548 in shotgun and fling. Requirements are 937 and 699 respectively.
3x ql 200 shotgun implants gets you, +210 shotgun and +42 fling giving 758 shotgun and 590 fling.
Wrangle + Offensive steamroller gets you up to 890 shotgun and 620 fling.
Dalja's ring and Ring of the Dolphin Spine (doc legchopper quest ring) gets you +24 fling giving 644 fling.
Finally adding Expertise to each gives you 910 shotgun and 664 fling leaving you 27 shotgun points short and 35 fling shot points short.
Ql 150 Medium Ranged Weapons Guide +3 shotgun. +14 shotgun and +10 fling from Essence of Behemoth and Prodigus Strength and Feline Grace giving 927 Shotgun and 674 fling. Still 10 shotgun short and 25 fling. +8 shotgun +7 fling from 1x Prodigus Strength perk and 7x Enhance DNA. Giving 935 shotgun and 681 fling. 2 shotgun short and 18 fling....
So I think you may just be able to get the shotgun but gonna struggle with fling shot :/ The rest you could get by implanting Abilities giving +88 agil and +55 strength. This gives enough Shotgun and just enough fling shot but ql 150 Light Ranged Weapons Guide will also give +3 fling. Now I actually do think it is possible but not worth it really
*Edit* I think Opifex is the easiest breed to do this with, Atrox and Nanomage will struggle more than Solitus. Opifex will only makes a very small difference as well. I also didn't include any buffing armor, I am not sure if some buffs flingshot but you can get ability buffing ones instead. 2nd Tier doc pants and gloves also add shotgun and fling, which maybe possible to just equip. For it not to be OE you need 750 Shotgun skill and 560 fling shot, i don't think this will be a problem once everything is reset like perks. So you can do it if you really really really want to.