You can't keep the URLs but you can definitely create URL redirects to map the old URLs to the new ones, more details here - https://help.shopify.com/en/manual/migrating-to-shopify/considerations#set-up-redirects
Yes, it is advisable to redirect the old URLs to new. If you do not then over a period of time you will notice in Google Webmaster that there will be many 404 not found URL error will popup. Not only that but if one visits the website and go to an old page then one will have this 404 error which can lead to a high bounce rate.
It is recommended to do 301 SEO friendly redirection.
If you have already pointed the domain to Shopify and no longer have access of Woocommerce store then you may search old URLs in google search result in case if require and even after few days you will notice those not found URLs list in webmaster, you may copy those and redirect to right pages.
In short redirection is good for SEO and website visitors too.
Hello there, You can use 301 redirect they are very friendly. While you are running migration from Woocommerce to Shopify, you can select this option as an additional option.. I know some provider give it for free if you choose their migration service. Find Woocommerce to Shopify Migration. Some top web having live chat are very useful you can ask them any question there. The service is also cheap and quick. Even you don't have tech skill, I am sure you can handle it well. Goodluck!