How to get rid of that initial dispatch before each CO-OP and Single Player mission?

Remove these files from your SWAT 4 folder:

Content\Sounds\ScriptedVO\AbombLoad_dis.ogg
Content\Sounds\ScriptedVO\ArmsDealLoad_dis.ogg
Content\Sounds\ScriptedVO\BarberLoad_dis.ogg
Content\Sounds\ScriptedVO\DNALoad_dis.ogg
Content\Sounds\ScriptedVO\FairfaxLoad_dis.ogg
Content\Sounds\ScriptedVO\FoodWallLoad_dis.ogg
Content\Sounds\ScriptedVO\HospitalLoad_dis.ogg
Content\Sounds\ScriptedVO\HotelLoad_dis.ogg
Content\Sounds\ScriptedVO\JewelLoad_dis.ogg
Content\Sounds\ScriptedVO\QwikLoad_dis.ogg
Content\Sounds\ScriptedVO\RedLoad_dis.ogg
Content\Sounds\ScriptedVO\TenementLoad_dis.ogg
Content\Sounds\ScriptedVO\VictoryLoad_dis.ogg

The same can be done for SWAT 4 TSS:

ContentExpansion\LocalizedContent\int\Sounds\ScriptedVO\Arcade_Load_dis.ogg
ContentExpansion\LocalizedContent\int\Sounds\ScriptedVO\Backstage_Load_dis.ogg
ContentExpansion\LocalizedContent\int\Sounds\ScriptedVO\Druglab_Load_dis.ogg
ContentExpansion\LocalizedContent\int\Sounds\ScriptedVO\HalfwayHouse_Load_dis.ogg
ContentExpansion\LocalizedContent\int\Sounds\ScriptedVO\Office_Load_dis.ogg
ContentExpansion\LocalizedContent\int\Sounds\ScriptedVO\Subway_Load_dis.ogg
ContentExpansion\LocalizedContent\int\Sounds\ScriptedVO\Warehouse_Load_dis.ogg

If you changed your mind and want them back, you can download them from here:

SWAT4: http://www.mediafire.com/download/tl3jlvcn3wbawby/Swat4-SOUNDS.zip
SWAT4TSS: http://www.mediafire.com/download/p8wg5fqeyy31pyk/Swat4TSS-SOUNDS.zip