If the LCD is a standard one, 1999 with a few annunciators and a sign, plus decimal points ( and probably a colon between 19 and 99) and has pins and not a zebra strip connection, then you probably can look at RS or other suppliers for a similar LCD display of the same size, as the layout for these is very standard, simply because of the need to have the pins laid out without any vias on the glass. Same height display will very likely fit there, though you might have the odd non original annunciator flag. If it is a Zebra strip version you probably will also find one that size that fits.
Otherwise the only way to remove the polariser is to first use a little heat to soften the adhesive, and then use a straight razor blade ( Minora blade as used in non cartridge straight razors, generally a cheap item sold in packs of 5 or 10) with some protective tape applied to the one half to protect your fingers, and gently slide under the edge to remove the plastic film from the glass. then you need some new polarising film for the display, which might be hard to get unless you are successful in removing it off another display.