Okey cokey, I'm going to give advice on a method I don't advocate, but you don't have a router.
Fitting Worktops.
Firstly cut the worktop that you intend to peel laminate edge off of to length we'll call this the Female Worktop. The other worktop will be the male, leave this over length.
Secondly, you will need to scribe your worktops to the wall, on a handled kitchen the overhang from carcass edge to the front face of the worktop is generally 40mm but possibly as little as 30 - 35mm depending on worktop with "600mm - 616mm".
If it's a Handless kitchen then the worktop over hangs the door frontals by 5mm only, carcass measurement does not apply.
Scribing worktops, you need to get the overhang the same down the entire length of the worktop. If you have more overhang at one end than the other when the worktop is pushed tight to the wall, you will need pull the shorter overhang out to get an equal overhang margin. Pulling the short end out will create a gap at the rear of the worktop to the wall at this point. This gap is your overall scribing distance.
So if your overhang on the right is 50mm, but on the left it is 40mm, you would pull the left forward to equal the 50mm margin, this will leave a 10mm gap at the back at this point, grab a 10mm packer or such like place against the wall with a pencil against the packer and drag the packer across the wall transfering the pencil line into the worktop this is your scribing line to cut to.
Once done, put the female worktop in its desired finished position, place the male worktop in its desired finished position on top of the female "normally 90 degrees" at the point the male crosses the female mark this position on both front edges. Remove male worktop.
Grab a combination square and a very sharp utility knife, put the combi square on the pencil line you marked previously and cut the laminate edge carefully with utility knife. Now you need a hairdryer and long nosed pliers, gently heat the laminate edge you want to remove, use the pliers to pull the laminate edging away from the worktop once you have about 10mm loosened use the pliers to roll the edging off whilst gently heating, keep the pliers away from the worktop edge.
Place male back on top of female in proposed finished position, with a pencil draw along the face of the female peeled worktop transferring this line into the male, this is the cut line for the male, once cut, cut dog bolts.
Don't use contact adhesive, if you can wait but Bushboard Complete, failing that use Colorfil.
I'm tired now. Good Luck.