I would not put the Silkies with your LF Cochins but, might think about it if they were bantam cochins. It would depend on the size of the newly hatched Silkies and how many. Also, it depends on the size of the brooder and if there was a way to block an area so the larger sized, older birds couldn't fit. The smaller chicks then could have a safe place.
How many Light Sussex and what age do you have? If only 2 or at most 3 and less rhan two weeks apart in age, again I might think about putting them together if there was a safe-haven for the smaller, younger chicks. You will have to use your best judgement.
I have mixed Silkies together with good results. One 3 week old chick with 5 new hatched. And most recently, 1 small 4 week old chick with 1 new hatched.
I have mixed chicks that were 5 weeks apart in my grow out pen by giving the smaller chicks a safe haven that the bigger chicks couldn't get to.
Dale-Ann