I'm not sure I 100% understand the details of the system you are describing, however the main point that you are asking is:
Do you know if there is any way to recover\rebuild the .dbf and .shx files from the shapefile?
Im assuming you want to recover attribute information that was stored in the DBF and the linkages to the .shp, in which case, the simple answer is no.
If using software like ArcGIS and you only have the dbf? won't work. Only have the shx? wont work. Only have the shp? wont work. Other software does not have these limitations, other software does.
Its possible to recover the geometry and generate a 'working' shapefile dataset which will show geometry only, but it will no associated attributes that were once previously associated with it. Tools are available which can recover the geometry only portion of the file (see @user30184 comments).
The DBF contains the attribute information. The SHP contains the geometry elements. The SHX is essentially an index/lookup between the shp and dbf files, linking the two files together.
With your specific scenario and system you describe, IF (and this is a big if) the .shp file is being stored as a blob object inside of Oracle, and the attribute information stored inside a simple table in Oracle, then you could potentially you could recreate your dbf file - but without the shx file, and without intimate knowledge of the data and geometry elements, linking the two back together is not possible.