In the latest version 3.5.1 of Bitcoin and Altcoin Wallets you can now write JavaScript code that executes on some wallets-related event.

For example, you could choose to set the default coin, once the coin information is loaded from the JSON API. Do this like so:

jQuery( 'body' ).on( 'wallets_ready', function( event, coins, nonces ) {
    if ( 'object' === typeof coins.BTC ) {
        wp.wallets.viewModels.wallets.selectedCoin('BTC');
    }
} );

There are full instructions on this in the documentation, under the Section Frontend → Frontend UI JavaScript event bindings. The documentation lists all of the available events, and sample code on how to enqueue your JavaScript file using wp_enqueue_script().