Yeah no, Dio has no chance over the Spectre. Time won't do anything to the Spectre as he's immune to time stops and ice won't do anything to him since Superman just touched him and his arm froze. The Spectre will most likely be aware of Dio's stand and can conjure up a mini sun to destroy Dio.
You may argue that because it is a mini sun it won't affect Dio but one of the Spectre's enemies, Eclipso is weak to the sun and the Spectre formed a mini sun to beat him. Dio has 0 chance of winning. Physical damage doesn't half the Spectre.