From SP, there are 2 ways to get to Corozal.
1. The Thunderbolt water taxi departs SP at 3pm daily and arrives in Corozal at 5pm, but check to see if it's operating because I've heard that it hasn't been making daily trips recently. The Corozal bus terminal is less than 1 km from the water taxi pier, or get a taxi for BZ$5.
2. Tropic Air or Maya Air. The Corozal air strip is a km or 2 south of town and the taxi fare should be BZ$8 (or $10) to get back to the bus terminal.
From Corozal, there are a few ways to get to Chetumal.
1. A taxi to the border should cost about BZ$25. After completing Mexican immigration, get a Mexican taxi to Chetumal for MX$70 (that's pesos).
2. A bus from Corozal to Chetumal costs about BZ$2. The bus terminal is not big and the staff is friendly & helpful. All the buses have the destinations displayed in the front window of the bus. The buses to Chetumal depart frequently (about every hour or so), but after about 6 or 7pm, the buses only go as far as the border/casinos and do not cross the border and go to Chetumal. If you go only as far as the border, you can get a Mexican on the other side.
3. Use a transfer service.
There is a new ADO express bus service from Belize City to Cancun. It departs Belize City daily at 7:30 pm; stops at Orange Walk (9:00 pm), Corozal (10:00 pm), Tulum (4:00 am), Playa del Carmen (5:00 am) and Cancun Airport (6:30 am). Arrives at Cancun bus terminal at 7:00 am. It does not stop in Chetumal.
Fares: BZ$55.00 to Tulum; BZ$63.00 to Playa del Carmen; BZ$79.00 to Cancun (one way).
You could get a water to Belize City and board the bus, or go to Corozal and board.
I don't think there are any flights bewtween Belize City and Cancun, but check with Maya Regional (Maya Island Air) because they did operate this route until earlier this year (they may have stopped in the low tourist season, and might resume later?)
I don't know about Aerocaribe, but there is a Mexican airline that once had flights between Chetumal & Cancun. I think they are currently not operating that route.http://www.mayair.com.mx/