The Kamino Sabredart is an instantly recognisable piece of kit that leads a Jedi investigator directly to its user.
Why would a professional like Jango use such a distinctive weapon when he could have used a cheap blaster or a slug-thrower that would have had zero chance of onward detection?
Kaminoan Saberdarts, in fact, were not easily recognizable. In a deleted scene (from where the screenshot is originally) in Attack of the Clones, an analysis droid at the Jedi Archives informs Obi-Wan Kenobi:
SP-4: As you can see on your screen, subject weapon does not exist in any known culture. Probably self-made by a warrior, not associated with any known society.
Also, if we can go along with the Legends, Wookieepedia says:
In Star Wars: Bounty Hunter Jango Fett uses these darts even though he hasn't become involved with the Kaminoans at the time, these darts may be similar darts which Jango later replaced with the saberdart.
So, Fett had been using Saberdarts for a some time, and he knew they could not be recognized; except by a former gunrunner and mine prospector, who just happened to know them from his personal past:
Dexter Jettster: Well, whattaya know... I ain't seen one of these since I was prospecting on Subterrel beyond the Outer Rim!
Jango Fett works for Dooku and Dooku works for Palpatine. Palpatine doesn't really want Padme dead (she is very useful for him, being Anakin's weakness). In fact he does everything to get them together after failed assassination attempt. What Palpatine really needs is that Jedi discover Kamino and Clone Army, in order to proceed with Sith Grand Plan culminating with Order 66.
Kamino was erased from Jedi Archives (in Legends it was Dooku before he left the Order) , to allow cloners some secrecy while creating the Clone Army. But now, this army is completed, and Jedi would have to be led to Kamino, without raising suspicion. And what better way then to create emergency where Jedi like Obi-Wan Kenobi, with lots of connections in underworld, would "unexpectedly" find trail that leads to Kamino. IMHO, Zam Wesell was set up to fail and that is the real reason Fett didn't try to kill Padme by himself - he would succeed, but then Clone Army would not be discovered. In worse, Military Creation Act would pass and Republic would have regular (non-clone) army which would be much harder to control .
Out-of-universe, Lucas is simply not very good in storytelling. He needed some reason to bring main characters (Anakin and Padme) back together and in spot light, but he also needed some reason to explain discovery of Kamino. Therefore, he invented this rather convoluted and illogical story with outsourced assassination contract and strange dart.
