The LEDs appear to be standard 7 segment LEDs that are used in old electronic games, old calculators, and anything that uses a seven segment display. Removing the old ones requires a vacuum solder sucker or solder wick braid. If you try to unsolder all the pins at once with just the soldering iron, you are sure to burn up the PC board. There are pin mounted and surface mounted designs, also, and they come in common cathode and common anode polarities.
Most any electronics supplier carries them. Most are interchangeable if they fit the hole pattern, but you have to make sure that they are compatible in terms of physical characteristics, voltage, and switching polarity. Some consumer more power than others. You are on your own when you try something like this. Maybe someone else has done what you are considering and will post here.
Here's a link to a similar display on Jameco Electronics web site. Jameco is one of the big players in electronic repair parts. My Provari looks like the digits are about .25" in height. Finding someone who has done it will be your best bet in getting the right parts.
http://www.jameco.com/webapp/wcs/st...=7-Segment LED Display &search_type=jamecoall