In case the OP would like to avoid the Orclike trait without altering the game; i.e., playing within the original parameters; Here is my advice:
1 - The Orclike trait has a no-going-back level of 1, so you will not be able to get rid of it once you have it, however, Orclike does have anti-traits: BloodHumour, PhlegmHumour, Rational, Guardian, and Artisan. If you have one of these anti-traits beyond the no-going-back level this should protect your general from the Orclike trait.
2 - The most sure-fire and convenient way to avoid the Orclike trait is to use armies with no general to exterminate/enslave cities. In the alternative you could designate one general, preferably one with poor governing traits, to be your go-to exterminator/enslaver. This general will get very bad influence, but likely also some impressive looting bonuses.
3 - Extermination is not the only way to deal with large cities and, if you want to play a men-of-the-west faction in character, you may wish to explore some other methods:
a - Plague: You can use an extensive spy network to acquire the plague from an afflicted city and
apply it large cities prior to acquisition. Be careful not to mix these infected spies with your own
cities and troops, and do not capture the city until the plague has run its course.
b - Black and True Numenoreans: These generals have a -10 to squalor and may make the difference in
being able to manage a newly acquired city. Probably a temporary solution until unrest drops since
this governor will cause population to continue to grow.
c - Have others do the dirty work: You can manipulate your allies and your enemies into doing
exterminations for you. The AI seems to exterminate with a great deal more prejudice than
necessary, so if you let the AI capture a large city it will probably kill off the population for you.
d - Rioting and Sabotage: The least effective due to the relatively small size of the map on this mod.
Only a viable option on the very periphery of empires. A combination of spy infiltration (a max of
three spies for this effect), sabotage of happiness and health/growth buildings, and conversion of
the population away from that of the controlling faction. Throwing in a siege should help. This
method is impractical, even on large maps, due to the expense of units involved and the limited
number of citizens which tend to be lost each round.
Exercising these options will slow down your empire growth considerably, but will also make the game considerably more interesting.