I want to run 8-ohm speakers on two different amps.
One came with 4-ohm speakers. (The 8-ohm speakers just sound better.)
The other came with 6-ohm speakers, which are long gone.

I understand that there will be some volume loss, but will such a substitution create a risk to life, limb or property?

More details. Model numbers will help.

One Set of speakers, two amps? You will need a switch or you will see smoke.

[Link: ebay.com]

1. Onn ONA13AV503 mini-stereo. Its OEM speakers are rated at 4 ohms. I have two Panasonic [M# SB-555] speakers rated at 8 ohms, 12W.
2. Aiwa CX-NAJ20U stereo. Its OEMs are 6 ohms. I have two Sears 2-Way [M# 564.92904551 ?] speakers rated at 8 ohms, 50W.*

*The manual for #2 says the surround-sound speakers can be 8-16 ohms, but I could not hear the vocals when played through there.

As long as the speakers are at or above the rated ohm load for the speaker outputs of a device you are fine.

Using speakers that have a lower impedance than the rated output of a device =
1) It might work fine because the device can handle a little more load than rated.
2) You will damage the outputs of the device (or it will keep shutting off to try and protect itself).

In your situation, you have 8ohm speakers, so those will work fine on any of those systems.

The Aiwa CX-NAJ20 = It only has stereo outputs (clearly labeled at the bottom). The "Surround-Sound" outputs on the RCA jacks, are a gimmick. Original the system came with 2 little additional speakers that plugged into there - limited bandwidth with a delay/reverb. Those are NOT real speaker outputs you want to use.

Thank you for filling in the gaps.

Follow-up:
The 6-ohm system continues to play with no obvious problems.

The 4-ohm system played well enough, but when I turned it off, I could not turn it back on again without leaving it unplugged for a short period of time. That problem went away when I brought back its OEM speakers.

That's weird.
But Onn is a Walmart brand and is pretty much bottom of the barrel (Fisher Price, Barbie's First Stereo, etc...).
What are the expectations here? Why are you messing with this junk? Just curiosity?

My wife wanted music in her work areas (kitchen & laundry). I was just trying to MacGyver what we had on-hand.

Addition information. The model numbers will be useful.

Amplifiers for two sets of speakers? A switch is required to prevent smoke from visible.

Post #3 is all the info I have.

You need something like these.

[Link: a.co]

[Link: a.co]

Thank you, but I have two different amplifiers (Aiwa & Onn) and two different pairs of speakers (Panasonic & Sears) available. There is no threat of a cross-connection.

To date, the 6-ohm (Aiwa) system is working fine (with the Sears speakers).

The 4-ohm (Onn) system had unexplained turn-on issues until I returned to its OEM speakers. Aside from its troubles in turning back on after being turned off, it played well through the Panasonic 8-ohm speakers.