Yes, ninjas were a real thing. No, they didn't habitually wear all-black pajamas and carry straight-bladed katanas - not until the 1980s, anyway. It's taken me years to decide it was okay to add a couple of decent quality "ninjato" to this website, but since I've started a Film and Fantasy section where I can cross-index them to the more traditional Japanese swords, here are a couple of select examples.
The main ninja clans/schools were the Iga and the Koga. This "Kouga Ninja-to" (manufacturer variant spelling) is made by Hanwei, who are known for their Japanese (and European!) sword-crafting. The hand forged blade is differentially clay-tempered 1566 high carbon steel, sharp and functional. The fittings are blackened/antiqued iron, with black same' and a cotton-braided wrap tsuka-ito. The saya is wrapped with rattan has a reinforced spike kojiri. This is top quality workmanship.
blade: 22 3/4"
blade width: 1 1/4" at habaki
blade width: 7/8" at 2" from tip
tsuba: 3 1/4" square
balance point: 3" from tsuba
weight (sword): 2 lb 5.0 oz
weight (sword and saya): 3 lb 4.0 oz