I think that the answer to the question "WI no Roe v Wade" would be the same as the answer to the DBWI question "WI no Bowers v Hardwick" whose DB scenario is a Bowers v Hardwick that anticipates OTL Lawrence v Texas.
Here we are with a map of sodomy legislation prior to Lawrence v Texas. Illinois struck its sodomy laws in 1962, therefore being light yellow color.
Golden yellow indicates sodomy liberalization in the 1970s or 1980s, mostly prior to Bowers v Harwick (1986).
Blood orange indicates a 1990-2002 date. They would be the states we'd really have to argue about if Bowers v Hardwick had anticipated Lawrence v Texas if we were talking about sodomy laws in a DBWI scenario where Bowers v Hardwick was decided as per OTL.
Red indicates all the states where sodomy was illegal until Lawrence v Texas.
What can we learn from OTL sodomy legislation?
Firstly, Roe v Wade only anticipated a proposed liberalization of abortion in most states. I'd even say that most states in golden yellow would have legalized abortion by the end of the 1970s, as it happened in most European countries. I even don't think that they'd restrict abortion again if Roe v Wade would ever be overturned, what I don't believe to happen. Yes, I know Planned Parenthood v Pennsylvania, but still, don't you think as well that, after almost four decades of abortion on demand availability, too many generations became used to easily mend their contraceptive accidents?
Secondly, the two Bible Belts, the greater in the Southeast and the lesser in the Rockies, would more or less have withered the trend. In that area would be very few states with Irish-style legislation (no abortion except at death risk), more with a Polish-style legislation (life risk, birth defects, rape) and many more with a German-style legislation (literally illegal, factually unenforced or overruled, streching a social indication to a factual abortion on demand). The shade of blood orange may be representative for actual state legislation to surprisingly vary among neighboring states of cultural proximity. Some may take longer, some may take faster, and it's often by coincidence. Or do you really think that Michigan really is to be more conservative than e.g. Georgia?
Thirdly, there would indeed remain some nastinesses that Roe v Wade swept away and some even weren't swept away in OTL. I remind that Florida law punished persons sponsoring abortion journeys to Mexico to pregnant minors who either don't have the parental consent for abortion or were rejected legal consent by a Florida court for being "too young to see the psychial problems arising from the guilt emotions to the aborted child". Now you could say that parents acted responsible when they prohibit their minor daughters to take an abortion. What would you say if parents wanted their minor daughters to abort the child against her will?
Fourthly, an absence of Roe v Wade won't assure an analogue not to come at a later time, after more states reformed themselves and when the court decision would practically rather serve as a territorial gap filler than as a real landmark decision. Such a delayed Roe v Wade would be less controversial and not be in any real danger if a Republican president has the luck of picking another "originalist" as a SCOTUS judge. Lawrence v Texas is not in any danger IMHO, an anticipating Bowers v Hardwick, at a time when gay saunas were closed in San Francisco to curtail the hot spots of inter-gay engagement due to the AIDS epidemic, would have been in danger.
Now the big question: I'm a pro-choicer. Do I support Roe v Wade or do I reject it in the way Ginsburg does as it radicalized otherwise unaware pro-lifers? I support Roe v Wade, because it makes life much easier as a girl in Alabama when you're, well, late.