Futa no, trans yes, but staying that way can be difficult if you're new to the game. The easiest non-cheaty way is to just develop a female figure for a while with the normal nightly transformation events and the breast & skin creams, and then use the physical-changes blocker spell (from the hobo downtown) so you don't lose your penis.
There are a few events to watch out for that will cause instant massive physical changes (e.g. AMI's birth control trial will give you female genitals, and there's an event in the park that will make your character fully male), so it's a good idea to keep multiple saves just-in-case.
You can use the cheat menu (particularly the "ring menu") or the actual body-changing ring artifact to have fine control over your transformations.
The potion lab in the mansion will also let you customize your body, but the effects are AFAICT always temporary.
Finally, one of the recent updates added superpowers (available through another AMI trial). It may take some save-scumming to obtain, but one of the powers allows you to transform at will. I haven't experimented with it much, so I'm not sure if it will do exactly what you want. If you want to get that power as quickly as possible, use the console cheat and enter the command
Code:
gs 'GenerateTraits','Assign',36
Edit: p.s. If your character presents as female, but has a big dick, most NPCs you can pick up in bars and such will usually react negatively if you tell them about it. Weirdly (this is probably a bug), if you just strip-down and fuck them bare, they never seem to complain at all. This may require the "skins only" trait you can get from watching pregnancy-porn (or the console command "gs 'GenerateTraits','Assign',4"), and I suspect it will change in a future version. It worked every time for me in v 0.11.6a.