You sound like a most considerate neighbor. But finding a saw so quiet
it will not wake a sleeping child is akin to a search for the golden
fleece and when you find one "fleece'd" is likely to be the
conclusion.

If you think the decibels generated by a brand new 15AMP motor cutting
thin air will wake the neighbors - wait 'till you put that meter up
against one cutting across some plys made of wood. Or, maybe you'll
make a garden shed and turn your blade 'round to slice through some
galvanized 5V Crimp - you are not allowed to do that near a cemetery!

My favorite is an Old Sears Worm Drive Saw - though I wish, at times,
it had the larger 1/8th inch thick aluminum sole plate as on an old
"Skill" saw my father-in-law left - not sure, but it may have been a
JC Penny!

That SEARS WORM DRIVE looks like the Milwaukee, etc etc as it is
simply re-branded.

As to the noise, well my wife makes me shut down at midnight because
of "the neighbors" but I think she is as worried about her lack of
sleep. And, up in the hills, my neighbors half a mile away report
hearing me working and can often identify the power tool I was using -
"What'r routing last night?"

Face it Woodworking is a noisy business, but somebody's got to do it.
And that somebody should seriously consider ear protection when
younger so as to assure a neighbors sawing will still disturb them
when they reach sixty or so.