.250 is the standard but I have seen 3/16 in some also. 3/16 sounds good for what you want and I would chamfer the hole to not have any sharp edges to fray the cord.
I wish I could invite you all down here for the fun. 100 knifemakers plus 35 tables of supplies for us will be available. Saturday only with a scheduled dinner and get together afterwards at the Courtyard by Marriott Friday night to get to know each other. I am going to enjoy this!
One thing also you can do is I glue one side of sheath and matching welt, when it is almost dry I align them together. I then use a small square faced hammer and hammer with over lapping blows. I then glue other side of sheath and welt then when ready apply them together. I hammer again back...
I start with a 50 grit then 120 then 400 grit pre heat treat on 154cm. AEB-L post heat treat I do 50,120, Trizact A65 then A45 and hand sand. Damascus I do A 30 pre etch. On 154cm after heat treat I do 120, trizact progression again.
I sand with an 80 grit belt then use an edger for the corners. I dampen the leather then rub with saddle soap to smooth , next a hard plastic piece to rub to smooth.
Then you are advertising in the wrong market and you are using a sheath maker who your need to do a search for a less expensive maker. You can make all kind of excuses about why not to do it.