I guess both FSW and CEC needs letter from employer if you are claiming for the points. And yeah i don't think claiming you don't have funds actually matters because if you are eligible for CEC and FSW usually they invite for FSW. I read a couple of people in the forum actually claimed they don't have funds and got invited to FSW. All the best ..Lets hope for the best.
(Getting a PR is better than rejection
so lets w8 and hope