Convert static php and html pages to wp pages and keep same URL

I have a couple of older well established small sites that have static .php and a few .html pages. I would like to convert these to WP but I would like to keep the original URLS. I can edit the page url but it ends in / I would like to make them end in .php or .html.

I know that I can use a 301 redirect but would prefer not to as these pages are old well established and heavily linked to urls.

Thanks