Pontificating about responses to an engine failure after take off in an aircraft not certified under CAR 125 or equivalent is futile.
One response only - Are you above Vmca by a good margin? & Are you above V2 by a good margin?
If both apply,[and the numbers should be assessed pre take off ] - commit to continue - [my idea of a good margin is 20%].
IF NOT-, commit to an emergency landing in the best area ahead.
Statistics pretty much verify that loss of control is fatal.
Only test piots have the skill and "corporate knowledge" to operate at the boundaries!!