Question: Did Peter Parker take part in, or have knowledge of what happened to the rest of the radioactive spiders? Were they disposed of or are they are still hanging around in a lab somewhere?

Answer: 
I'm not sure whether this was retconned (and how many times...), so I'm going by what was shown on Spidey's first appearance, on Amazing Fantasy #15.

According to that, there were no other radioactive spiders. One single spider was accidentally irradiated, and it has bitten Peter Parker:

![Radioactive spider biting Peter Parker](https://i.stack.imgur.com/xhKad.jpg)

Apparently, spiders were insects in 1962

The spider was dying due to the amount of radiation it absorbed, so we can assume its body was disposed (by the janitor?).
If we're speaking about the spiders [plural] from the Sam Raimi trilogy, its somewhat unknown. It *Was* said that traits from various spiders were taken and recombined into "These 15 genetically altered super spiders" to which Mary Jane pointed out "There are only 14; one's missing," [not counting the one that escaped and bit Peter]. But after that school visit, I don't believe any further thought or mention was given to them, even to finding the one that escaped.

To be fair, these weren't "Radioactive" spiders, and the one that bit Pete just wondered off. Thinking about it, this is a *Severe* ball drop on Peter's part; presuming they were all genetically and structurally identical, **any one of those spiders** could then imbue someone *else* with Peter's powers! Not an ideal situation....