Plenty of folks would tell you that glyphosate is hazardous/toxic, and potentially carcinogenic
And they would be wrong, at least about it being carcinogenic. Of course it is hazardous/toxic if you do something stupid like drink it, in normal use not so much.
Glyphosate, under various names, has been in use in for decades and has been used by many millions of people. All the studies that have looked at it have found no connection with ill effects. Except for one study in the US where they found a slightly raised level of one type of cancer in agricultural workers who
claimed that they had always done everything right and had never cut any corners.
People making claims about glyphosate are simply falling for the
post hoc fallacy.
OTOH diesel, etc, are clearly bad for the environment. Spray plants with glyphosate uphill from one pond and pour diesel, old oil, etc uphill from another one and see which pond is affected.
Either way if I was the OP I would just pay someone to trim the laurel hedge once a year, it's not a big job for someone who has the kit. Provides a home for wildlife, absorbs carbon, and it will outlive a fence!
Nice idea in principle but the big problem, IMO, is that it is laurel. There are different types but many do not make nice hedges and many tend to spread.
If making a hedge I would cut it back severely, make some ground level gaps and plant a variety of (preferably fruit & nut bearing) hedging plants in the gaps. Repeat that the next winter (or maybe two) and it will create a much nicer looking and more beneficial hedge.