J and B said circular saw with a fine blade wouldnt cut the shelf properly. I guess he means must be a plunge saw. Curious, why is a plunge saw better than a circular saw?
You actually have several problems to overcome. Firstly, can you actually get your saw into the space without the motor or the base fouling on something?
Secondly, how do you prevent your fine saw blade from chipping the edge of the laminate? A rail saw can do this when cutting from the top surface because there is an anti splinter strip along the edge of the rail - and in addition they often have the facility to do a 1 to 2mm deep scoring cut before making the main cut which specifically deals with break out. With a conventional saw, fine blade or not, you need to cut from the underside to guarantee a good, splinter free cut. But even a rail saw can't cut all the way to the wall
Thirdly, how, assuming the saw will fit, do you intend to finish the cut to the wall neatly? The last few centimetres that the saw blade just can't reach. A jigsaw won't reach fully to the wall either and in any case won't be a neat cut (unless you happen to possess a P1cc), and a multitool will give you a godawful rough cut. So the only way to achieve a decent scribed edge may be to mark the scribe, remove that section of worktop, make the cut (from the underside, given that you have a cordless rip saw, not a rail saw), then reinstate it. But if there is a mason's mitre at the other end of that worktop and the joint has been glued, then that may not be easy or even possible. In any case, even if it hasn't been glued the joint will need to be sealed water tight when the top is replaced as will the newly scribed end
What is certainly the case, is that if you chip the top or the joint subsequently blows you
will will be liable for supplying and paying for installation of same (because it is unlikely you'd be given the opportunity to do it yourself in the event that you screw up).
If you haven't figured all this out already, then you are out of your depth, I'm afraid, and should admit you are and walk away before upsetting your client even more than the builder already has done. Kitchen fitting is not for the inexperienced - at least not if you are being paid to do it and ate expected to deliver a flawless professional result. I am trying to be dispassionate in this and to avoid inflamatory language