I've found a better solution which works generally and not just for the portal:

odoo.define('your_module.name_and_signature_extension', function (require) {
"use strict";

var NameAndSignature = require('web.name_and_signature').NameAndSignature;

NameAndSignature.include({
    init: function (parent, options) {
        // Ensure options is an object to avoid errors
        options = options || {};
        // Set default mode to 'draw' if not provided
        options.mode = options.mode || 'draw';
        // Call the original init function with the modified options
        this._super(parent, options);
    },
});

});

put this snippet in a seperate modul at static/src/js 

and load file in web.assets_frontend section in manifest

"assets": {
	​"web.assets_frontend": [
    	​"/your_module/static/src/js/name_and_signature.js",
	​],
}

with this code the default_mode is set to 'draw'

I found a solution:

Edit this file

portal/static/src/js/portal_signature.js

change in line 161:

'mode': this.$el.data('mode'),

by

'mode': 'draw',

and add this later to the same file:

var style = jQuery('');
jQuery('html > head').append(style);