Here's how I would cut this dado using a hand saw and chisels. The chisels I used are a set of Irwing Marples I picked up for $60 and replaced the blue plastic handles with wood. I also had to do a fair amount of flattening, honing and grinding to remove the factory tool marks. But hey, they were $60.
First I marked my perimeter with a knife and highlighted with a Sharpee.
Here is one of the chisels. This is 1" wide but I did not use this one for this project. Instead I alternated between a 3/4" and 1/2" chisel depending on how the cutting felt.
I cut the boundaries and then kerfed in with the saw. This makes waste removal easier and more controllable.
If you cut across the grain I find the 1/2" works best.
If skewing I will use either the 3/4" or the 1/2" depending on how easily it cuts. Please make note of grain direction and remove the waste gradually. Generally hogging out massive amounts of wood at this stage can chip out in huge chunks and can run too deep. I use light taps with a wooden mallet.
After I get down to about the last 1/8" the mallet gets put away and I prefer to pare down to the final depth. Skewing when I can and paying careful attention to whether I'm cutting with, against or across the grain. Take your time and don't rush or you'll take out chunks.
Here are the two chisels I used with the finished product.
It is not completely perfect but will still be a nice solid joint. The small knot had to be worked carefully so it didn't chip out. I figure that after taking out all the interruptions I had it took about 5 minutes start to finish. Of course, if you use a router to clear out the waste it goes considerably faster.