Yes, in general this should work. I never had issues while braiding free handed, mostly 6 strand round or 8 strand square, but I have never done that on a marudai or with a card.
Hints:
- reduce the core as smoothly as you can. If using thick strings as the core, consider removing parts of the strings if possible or, with paracord, partial gutting.
- If you use thin strings in the core, instead of cutting directly you can also pull it out of the core, let it dangle loose and cut close to the braid when finished. There is a risk of having an irregularity where the core left the braid.
- For me, braiding while tapering is easier when I had a good amount of tension, i.e. the mantle is dense and not springy.
As always: when not sure, make a sample. It's time well invested
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Also consider: What is the function of the core and where does it come from? Does it carry any load or is it more a filler / hiding place for no longer used threads? If it's the second option, don't worry as long as you taper smoothly. If it's the first option, then I would not do it or at least make a sample, braid tight and dense and leave the core long enough in there for sure.
There is also a little bit of something here:
http://slinging.org/forum/YaBB.pl?num=1509416090/0Good luck!