In my experience...as long as you are grafting a Plum on a Plum you should be all set and it should graft for you.

Let us know how it works for you...I can't click on those links you offered for the tools.

I'm pretty sure if you're grafting a Prunus on a Prunus, it'll take. I'm not sure what you mean by nastyness of the Cherry Laurel but if you mean its tenacious growth habit, that's nothing unusual and shouldn't make a difference. They usually use very tenacious rootstock for grafting less tenacious plants onto, like Rosa multiflora rootstock for cultivated multiflora roses.

You could try this question over on the Fruit and Orchards Forum where there are some very experienced grafters. Are you hoping to graft an edible plum onto the cherry laurel? I have no idea if it would work or not but cherry laurel is poisonous in all parts. Don't know if that would make a difference.

If you go to You Tube, there are a lot of videos on grafting also. Do a search for fruit tree grafting. There are tons of videos there. I was quite interested in the T-Bud grafting for grape vines. Amazing video and very useful to me at this moment. I accidentally snapped 2 cordons on 2 vines and my vines are lopsided. That is grafting vitus vinifera onto vitus vinifera. Not sure if you can graft plum onto cherry, but they do make those fruit cocktail trees with a few varieties on one trunk, so it's probably possible.