Splicing Maffiloi

You could try the soft fid method https://www.youtube.com/watch?v=UZkwS_HVn6s to get what you are after. Might need a bit of stitching to get enough strength. 

Or you could attache your thin dyneema piece in with a locking brummel. Here are some rough directions if you need them. Start by putting the swiftcord through the thin dyneema about a fid length from the end of the dyneema, pull through at least 2 fid lengths, take the other end of the dyneema and put it through the swifcord about a fid length from the end of the swift cord. Pull the main bits of the swiftcord and dyneema away from themselves and the brummel will lock. now the tricky part. The short dyneema end needs to be threaded down the inside of the swiftcord which isn't too difficult if it is thin, however the thinner it is the harder it is to thread the swiftcord end inside the dyneema. A really open weave helps (one where when you push the rope it opens up and has a big space inside it). That will get you the thin line connected to the thick line. then splice away like normal*

 *lots of difficulty

option 2 is an end to end splice without the lock and that can be seen here https://www.youtube.com/watch?v=Q6patBi3aEo the whipping might get stuck when you try and splice with it though so maybe just stitch through over the joint a couple of times to hold it together.

Hope some of that helps