I'm Miles from the Social Care team at Shopify. You'll be happy to know you're able to set up shipping without needing to reply on price or weight - though you will need to select one in order to set up the shipping. I'll explain below.
Flat shipping rates charge a specific amount for shipping at checkout. You can create flat shipping rates for any order within a shipping zone, or only for orders whose weight or price is within a certain range. For example, in a shipping zone for Europe, you could set a flat rate of $10, and another flat rate of $5 for orders that are over $50.
In your case, let's say you'd like to charge $5.00 for standard shipping and $10.00 for express. To set this up, you'd add in a rate with no conditions and just label the 2 rates as Standard and Express.
From your Shopify admin, go to Settings > Shipping and delivery.
Next to the shipping profile that you want to add a shipping rate to, click Manage rates.
Next to the zone that you want to add a rate to, click Add rate.
Enter the name and amount for the rate.
Click Done, and then click Save.
Once you're done, it should look something like this:
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