In the 29th minute Anthony Tonkin was shown a second yellow card for a lunge on Gareth Ainsworth, having already been booked for a foul on Bruno Andrade.
A superb first-half double save from Jordan Archer, twice denying Peter Vincenti, was the closest either side came to scoring in an end-to-end encounter.
The hosts came into the game on a three-match unbeaten run and pressed early on, Kieron Cadogan looking threatening down the right. Aldershot should have gone ahead after 15 minutes through Vincenti before Danny Hylton blocked team-mate Craig Reid's shot on the line.
Jamie Young pulled off a one-handed save to deny Ainsworth from distance before Wycombe skipper Dave Winfield fired over from six yards after Andrade's right-wing cross.
With Wycombe pressing late on Dennis Oli nodded just wide from Josh Scowen's free-kick before Young pushed Matthew Spring's free-kick wide to earn his side a point.