Presumably Edward IV would have made dispositions for the occasion of a female succession - Elizabeth might well already be married off to some beloved cognate. There would therefore be a candidate, or if she's not yet married, a selection of candidates already eyeing up Elizabeth as a means of obtaining the English crown, who would be positioned to check and move against Richard in the immediate aftermath of King Edward's death.
There would be no need for Richard to serve as Lord Protector - Richard would never intercept the young King on his way from Ludlow or any of that business - the Queen would probably be fairly near to/in London for her confinement - the Greys and Woodvilles would be better positioned in/near the capital to dominate the Regency.