Do an action from ViewModel right after ShowDialog

I have a ViewModel like this:

public class WelcomeWindowVm : ViewModel
{
    private ViewModel view;

    public WelcomeWindowVm(){
        this.View = new LoginVm() { 
            Completed += (o, e) => {
                this.View = new OtherVm(e.User){ 
                    Completed += (o, e) =>; // and so on
                } 
            }
        };
    }

    public ViewModel View {
        get {
            return this.view;
        }

        set {
            this.view = value;
            this.OnPropertyChanged(nameof(this.View));
        }
    }
}

LoginVm is another Viewmodel whose Completed event is triggered when a Command on it is completed (The event is only triggered when correct login credentials are used). OtherVm is another vm whose completed event is triggered for whatever reason.

I render the View using a DataTemplate. For example:

<Window.Resources>   
   <DataTemplate DataType="vm:LoginVm">
         Textboes and buttons here
    </DataTemplate>
    <DataTemplate DataType="vm:OtherVm">
        ...
    </DataTemplate>
</Window.Resources>
<ContentControl Content={Binding View} />

The DataContext of this window is set to WelcomeWindowVm class above, before ShowDialog.

This works well. When the Window is shown using ShowDialog, LoginVm is shown. Then OtherVm when whatever task of LoginVm is completed, and so on.

Now I thought of converting the Completion stuff to Async/await pattern. The LoginVm now looks like this:

public LoginVm{
    ...
    private TaskCompletionSource<User> taskCompletionSource = new TaskCompletionSource<User>();
    ...
    // This is the Relay command handler
    public async void Login()
    {
        // Code to check if credentials are correct
        this.taskCompletionSource.SetResult(this.user);
        // ...
    }

    public Task<User> Completion(){
        return this.taskCompletionSource.Task;
    }
}

Instead of this:

public LoginVm{
    public event EventHandler<CustomArgs> Completed;

    // This is the Relay command handler
    public async void Login()
    {
        // Code to check if credentials are correct
        OnCompleted(this.user);
        // ...
    }
}

So that I can use it like this:

public WelcomeWindowVm(){
    var loginVm = new LoginVm();
    this.View = new LoginVm();
    User user = await loginVm.Completion();

    var otherVm = new OtherVm(user);
    this.View = otherVm;
    Whatever wev = await otherVm.Completion();

    //And so on
}

But I can't use await in a Constructor and even if I use an async Method for that, how will I call it in another class after calling ShowDialog since ShowDialog blocks?

I think using an async void will work. But from what I have heard, it should be avoided unless I am using it in an event handler.

Maybe use an async Task method but not await it?