Yes you can. There is a few steps you need to take, but then you can basically mimic all console behaviors from your own aspx-page.
First of all you need to include the necessary C1 Console javascript frameworks on your page. Do that by calling ScriptLoader.Render("sub")
and write the result on your page. You would also need to include this javascript on your page https://github.com/burningice2866/CompositeC1Contrib/blob/master/Teasers/Package/content/Composite/InstalledPackages/CompositeC1Contrib.Teasers/teaserConsoleFunctions.js - its some wrapper methods which are able to construct the javascript objects needed to call C1's webservice methods.
When that is setup you can trigger opening a Edit Workflow by calling the executeAction
javascript method via a link containing the necessary ActionToken and EntityToken like this https://github.com/burningice2866/CompositeC1Contrib/blob/master/Teasers/Web/UI/TeaserHtmlHelper.cs#L65.
Its important to understand that everything in the C1 Console in based on these tokens. You don't edit something based on its id but always based on the EntityToken the something is represented by.
And what you want to do, whether its edit something or delete it, that thing you want to do is represented by an ActionToken. So to be able to edit something, you need an EntityToken for that something and a ActionToken for the Data Editor.