Sure you can use your dump file.

In order to change tablespaces, you will have to:
1. create users on target database
2. dump structures to an indexfile
(imp system/manager file=yourfile.dmp indexfile=yourfile.sql full=y )
3. edit yourfile.sql and remove the REM's
4. go through every table and re-assign the tablespace (or use global search & replace is you are comfortable)
5. check for connect statements in yourfile.sql (either connect to correct user or get rid of them entirely)
6. run yourfile.sql to pre-create all the structures
7. import your data with ignore=y

That said, it's going to be REALLY slow because along with your tables being pre-created, indexes have also been pre-created. However, it works.