I've solved this in the past by just show the payment sources, and allowing the user to delete existing payment sources:

{% set paymentSources = craft.commerce.paymentSources.getAllPaymentSourcesByUserId(currentUser.id) %}

{% if paymentSources %}
    <table>
        <thead>
            <tr>
                <th scope="col">
                    Card details
                </th>
                <th scope="col">
                    Actions
                </th>
            </tr>
        </thead>
        <tbody>
        {% for paymentSource in paymentSources %}
            <tr>
                <td>{{ paymentSource.description }}</td>
                <td>
                    <form method="post">
                        {{ csrfInput() }}
                        {{ actionInput('commerce/payment-sources/delete') }}
                        {{ redirectInput(entry.uri) }}
                        <input type="hidden" name="id" value="{{ paymentSource.id }}"/>
                        <button type="submit">Delete</button>
                    </form>
                </td>
            </tr>
        {% endfor %}
        </tbody>
    </table>
{% endif %}

You can then show a form to add a new payment source:

{% set customer = craft.commerce.customers.getCustomer() %}
{# 
    Note: this next line fetches a single subscription - if you support multiple 
    subscriptions, you'll need to do it a little differently 
#}
{% set currentSubscription = customer.getSubscriptions()|first %}
{% set plan = craft.commerce.plans.getPlanById(currentSubscription.planId) %}
{% set gateway = plan.getGateway() %}

<form method="post" accept-charset="UTF-8" autocomplete="off" novalidate>
    {{ csrfInput() }}
    {{ actionInput('commerce/payment-sources/add') }}
    {{ redirectInput(entry.uri) }}
    <input type="hidden" name="gatewayId" value="{{ gateway.id }}">

    {{ gateway.getPaymentFormHtml({})|raw }}

    <button type="submit">Add card</button>      
</form>

This is probably the simplest answer to your question, though you can get creative with how you present the payment sources and the add card form to the user.