Howdy,
Most watches have spring bars and you use a tool with a forked end to pry the moving end of the bar in, so you can remove the strap. This can be easy or VERY difficult. It just depends on the watch and strap. However, I wouldn't use a toothpick as it will likely break off in the lug.
Some Blancpains have a solid strap pin that is pressed into the lugs rather than a spring bar. I can't say for sure which you have there in the photo as I haven't changed a strap on it.
But this is what I need for straps and bracelets, and I'm a small-time watch repair guy.
I'd suggest you get a watchmaker to change it while you watch, and have him show you what to do. Then you won't mess it up when you go at it.
Cazalea