You don’t have to transfer your domain registration to Hostmoster, if you just want to host website on hostmonster and leave the registration to original domain registrar.
Assign the domain in Domain Manager and follow instructions in your Hostmoster account. Login to registrar account and change Nameserveres to point to Hostmosnter.
NS1.HOSTMONSTER.COM
NS2.HOSTMONSTER.COM
It generally takes a day or more to reflect changes. Your website should be live with Hostmonster once change has taken place.