You can make a hole lot more of 1.5mm (1/64")wood. You should consider to make it a big stack (depends on how fragile the result will be).
I do also use this thin wood and I usually stack it to a massive 12 layers, which gives you a stack at about 3/4". It's not hard to cut that, you can use a #1 blade for it.
and yes - tape is best. The wood is surprisingly stable, it wont break if you peal off the tape with a bit of care.