Mindflayers could create human spies and gather information.
Target the ruling class first using Lilims, Dark Priests, Kunoichis, Nurarihyons, Kejourous, Living Dolls... etc., to turn them into a fifth column within human society.
Have Dark Priests corrupt the different churches from within by posing as pious women.
Have the Sabbath infiltrate and assimilate pedophile rings. These are already actively hiding, and could be easily turned.
Infiltrate disguised Kejourous, Succubi, Nereids, Dark Elves, Jorogumos within already existing organized prostitution mafias, and have them take over.
Infiltrate drug trafficking criminal organization, take them over and use them to distribute monsterization inducing substances.
Send infiltrators and start monsterizing and incubizing people. Isolated corners in undeveloped countries should go first.
Nurarihyons, Kejourous and Dark Mages could move freely even in developed countries without even using magic, and they could monsterize women without being detected... If they target girls who are attractive to begin with, people would barely notice the change (remember, mamono have innate spells to keep men they aren't targetting from noticing how attractive they are...).
Trolls, Doromes and Gnomes could create farms that produce tainted foodstuffs and start distributing them...
Matango spores could be spread around in the air in cities close to swamps and jungles.
Nereids could kidnap women from coastal settlements and monsterize them.
Dark Elementals could slowly start to taint the envirnment.
Giant Ants allied with Dwarves could dig whole subterranean cities and hide whole armies there.
Once humans notice something is going wrong, unleash a crushing attack with Dark Matters, Ice Queens, Pharaohs, Nine-tailed Youkos, Doromes and Dark Elementals working with gangs of Large Mouses, Werewolves, Succubi, Demons, Devils, Nereids, Arch Imps, Matangos, Dark Slimes, Ropers, Parasite Slimes, Cursed Swords, Ushi-Onis, Zombies, Mummies, Wights, Dragon Zombies...etc., to monsterize the greatest cities in the world, sending the most powerful countries into disarray.
Avoid combat, target the civilians; the cops won't shoot against their own families once these are monsterized.
If combat can't be avoided, send Zombies, Mummies, Oshimushas, Ghosts, Vampires, Living Dolls,Slimes, Ushi-Onis and other bulletproof monsters against policemen armed with mere guns.
If somebody manages to organize an army and send them to lay siege to the corrupted cities, use Dark Matters, Dark Elementals, Sirens, Ghandarvas, Matangos and Mothmen to gradually corrupt them so when they reach the cities they will start having sex rather than fighting.
Use bulletproof monsters for hit-and-run attacks against soldiers, raping them and escaping before bombs, flamethrowers and heavy machine guns cand be deployed.
If they start bombing the cities, order the monsters and their husbands to start havign sex. Monsters are invulnerable while having sex, not even nukes could hurt them.
Target the civilians managing communications, industry and energy sources (oil, electricity, nuclear...etc.) to cripple the defense of human nations.
Now, this way a few mamono will probably die, but losses can be minimized...
If you want to achieve zero losses, use only disguised or human-looking infiltrators and monsterize human women only into Majins like Dark Mages, Nurarihyons and Kejourous, and humanity will find itself without women before even realizing what is happening. They will probably consider it a strange "illness" that makes women younger, healthier, lustier and more attractive and will try to research it, but many people will see it as a good thing and won't try to stop it (they won't notice baby boys aren't being born until it's too late..).