I would reccommend a fixed bladed stanley knife for general grafting work - the blade is very sharp and dosen't wobble! Most temperate wood is much harder than tropical fruit trees. Hte video is very good - though professiionals do make cutting perfect wdges look very easy (Soft wood also helps).
I would buy some grafting tape from a horticultural supply store if you are thinking of doing more grafting, modern tape is very stretchy and self locking and should be impregnated with anti fungal agents to lower the risk of diseases getting into the wound. The tape also helps stabilise the join as cleft (wedge) grafts are weak and take many months to strenghten up.