Also, tires have different profiles. Meaning, some are more squared off, or have lugged side knobs (like the one in your photo) that add to the width of the tire at edge of that lug or 'squared off' point on the tire.
If the cream colored tires are more of a cruiser tire, with a round profile, the tire will have more of a uniform shape with no 'edge'. The width of the rim mostly dictates the height of the tire or 'tallness'. On a wider rim, the tire will be more flattened out and not as tall. On a narrower rim, the tire will have more of a 'light bulb' shape and sit taller off the rim.
Like @toro1978 said above ^, if width is your problem fitting in the stays, then keep a narrower (original) rim, and go for a more rounded profile tire than the square / lugged one that is pictured. Do you have photos of the cream tires you are considering?
If the cream colored tires are more of a cruiser tire, with a round profile, the tire will have more of a uniform shape with no 'edge'. The width of the rim mostly dictates the height of the tire or 'tallness'. On a wider rim, the tire will be more flattened out and not as tall. On a narrower rim, the tire will have more of a 'light bulb' shape and sit taller off the rim.
Like @toro1978 said above ^, if width is your problem fitting in the stays, then keep a narrower (original) rim, and go for a more rounded profile tire than the square / lugged one that is pictured. Do you have photos of the cream tires you are considering?