I think wood glue is most harmless type [1], and you do not need as much as it shown in video for the presentation purposes.

On the other hand, maybe friendly (non-glue) version would be with the contra-screw or clicking mechanism at the end. But it would be very hard to maintain lock while you cut the pencil/s pass the joint.

[1] https://en.wikipedia.org/wiki/Wood_glue "It is chemically similar to edible gelatin and is non-toxic if ingested."

But on the other hand you have different types: https://impressionsofaholobiont.com/2018/09/03/non-toxic-wat...