so imo if you actually try to worldbuild, and you want to maintain a "primary sex" and then a "secondary gender" (rather than creating a universe where there are 6+ different sexes), then omegaverse would be more like different hormonal balances. so rather than all female alphas having dicks, here's some possibilities:

• female alphas have external female organs, but lack the internal ones. they would still go into a rut. prob the most boring one, but possible.

• female alphas have external female organs, and internally their body develops so that the are more likely to produce large amounts of juices/cum, and that is able to impregnate female omegas. no difference externally though - impregnation has to happen by putting it in with fingers or other tools. (i have an oomf who has written omegaverse yuri of this kind!)

• same as above, except when in rut, female alphas also have enlarged clits. not enough to fully insert/be mistaken as a dick, but enough that they could maybe like rub the cum inside

• ok this has never been done afaik because omegaverse is so wolf-inspired, but i do see people give a/b/o to alien races, so why not do alpha tentapussy??? tentacles are sexy... then she can really knock her omega up and there are zero dicks involved!!