move my current wordpress site to the new one on the live internet

hi,

my webhost installs its own version of wordpress for me. so I can see it in mydomain/wordpress. viewing with filezilla I see my wordpress in the left window and theirs in the right window. Of course mine has content and theirs does not. so can I just delete theirs and upload mine and that will work? Then is to change all the urls using velvet blues or something else.
I have also emailed my webhost asking about this but they tend to answer with not-too-helpful replies