| Motorway (Motorväg and Motortrafikled) riding with a moped is as forbidden as riding a EU Class 1 moped on a walk/bike path/lane here. Most police would probably look harsher on that than riding <responsibly> on the walk/bike path.
Not knowing exactly where from/to the whole route goes, so it may be inconvenient; but looking at the map it looks possible to detour round the hospital and ride on a more rural road west of the motorway. But if you need to cross over to/from the east of the motorway up by point At, hat would be problematic. There are small roads on the east side as well, but the detour is definitely longer.
Maybe a check with the local police on their views on the issue (course, lessens the chance of getting away with a warning first time caught...) | 
