As others said no reason to add it to secondary, just expect it to mellow a bit from the time you bottle to when you drink it.
How are you going to use multiple types of coffee when adding the cold brew at bottling time? Are you going to fill the bottles with a specific amount of coffee and then fill the remainder with beer? Or, are you going to add coffee to your bottling bucket, transfer say 1 gal of beer to the bucket, bottle, then repeat those steps 5 times for 5 different types of coffee? I just used 1gal and 5 types of coffee to explain, no clue how many types of coffee you plan to use
Just my 2 cents on this though, I prefer beers that use whole beans added into the "secondary" for 20-24 hours. I think this gives the best coffee flavor and aroma and seems to have the longest "shelf life." I have never added coffee in the boil, but have tasted beers from others that have and it becomes to acrid and harsh for me. Cold brew fades too quick for my liking and seems to get lost easily, depending on the style and strength of other flavors. Coarse ground in the secondary seemed to extra some tannin like flavors the one time I tried it. Those are just my experiences, because of that I have used whole beans, 20-24 hours in the primary, in 4 different beers, with consistent results. A local brewery that does a coffee brown ale every couple months with different beans each time, uses the same method, whole beans for 20 hours and each time has a roughly consistent coffee flavor to it. I say roughly consistent because depending on the type of beans they use you'd expect some to be stronger or lighter depending on the "style" of coffee.