If this were my project, I'd just use my old Craftsman hand saw that I inherited from my Father-In-Law. Of course I would ensure that it was sharp, and set properly, but the biggest issue I see is technique. You didn't say how large the original table is, nor how long the cuts would be, so knowing how to properly hand saw a long cut might be an issue. As mentioned earlier, having a good hand saw available is always a good tool to have around, no matter how many power saws you have. I often reach for a hand saw and my bench hook to cut off a board instead of the table saw or band saw. Making a good cut with a hand tool is especially satisfying.
I've gone out to find myself. If I return before I get back, have me wait for me.
"Sawdust is Man Glitter"