Both are Async tasks, means they should wait for the task to execute any code after that,

there are several ways to handle this, but one of the easiest i can suggest is this one (with modifications i made): Important: i will make this suggestion basing on the given chunks of code, this does not mean this is the only solution.

Http request logic (basing on promises):

/**
 * the Http delete request to the API
 *
 */
deleteHttpRequest(url, headers){
    return new Promise((resolve,reject) => {
        this.http.get(url, {"headers": headers})
                    .map(res => res) // .map in this case has no sense you can remove it
                    .subscribe(
                       data => {
                         console.log(data);
                         if (data.status === 200) {
                           resolve();
                         } else {
                           reject(data.status);
                         }
                        },
                         serverError => {
                           reject(serverError.error); // basing on HttpResponseError
                         }
                        );          
                });
     }

}

Confirm popup

/**
 * Confirm before delete
 */
confirmPopUp(confirmCallBack, cancelCallback){
  Swal.fire({
    title: 'Are You Sure?',
    text: 'Deleting Service Team Detail',
    icon: 'warning',
    showCancelButton: true,
    confirmButtonText:('Yes, delete it'),
    cancelButtonText: 'No, Keep it'
    
  }).then((result) => {    
    if(result.value){
       confirmCallBack();  // <======= Here we will execute Http request      
    } else if (result.dismiss === Swal.DismissReason.cancel){
       cancelCallback();  // <======== Here you can do whatever you want after canceling your delete action.
    }
  })
}

Put all in one:

/**
 * Call popup confirmation then execute logic basing on confirmation status (confirm : execute http Request,  cancel: do whatever you want)
 */
executeHttpAndGetResult() {
  this.confirmPopUp(
    () => {     // when confirmed we will call deleteHttpRequest (confirmCallBack)
    this.deleteHttpRequest(url, headers)
        .then(
          res => { // when delete successed  
            Swal.fire('Deleted!','Your imaginary File has been Deleted', 'success');
        .catch( // catch will be called whenever data.status !== 200 or there is a server Error returned.
          error => {
         // display an error popup or whatever
          }
        );
    },
    // when confirmation was canceled what we will do (cancelCallback)
    () => {
     // @todo
     } 
  );
}