Seems a shame to dismantle your Giant to use the parts (you'll not be able to use the gears [duh], rear wheel, chain, rear brake, chainset [possibly]). Why not just sell the Giant and buy 2nd hand parts for your fixed/ss build?
keep both bikes. that way you have one geared, one fixed. perfect.
keep both bikes. that way you have one geared, one fixed. perfect.