The process I've both used & seen used by conservators is sometimes a very slow go , using small thin (but not sharp) tools , sim to those used for sculpting clay & an extra-fine (atomizing) distilled water sprayer , @ the pace of around a sq. centimeter per min if possible ;
sometimes a bit of gentle quick-drying (daubing) with clean cotton cloth is part of the process , and all 'wet-work' should be done with the photo always facing 'up' .... think of it as if you would if you were trying to open a sealed envelope & were trying to make it seem as if it was not tampered with at all ......... & that's about as close as I can get to describing the gentle touch required for the process .
One must first know the 'sort of' dissolution/loosening rate for the adhesive used , in order to time the drying/wetting/separating cycle for this type of work .
Always start in a corner of the 'valuable' area & progress to the opposing corner , so that if & when you get that far , you sorta peel-it-back as if turning a page in a book , rather than diagonally .
Conservators (real ones) use a rate table , for pricing exactly this type of work , per sq centimeter - so you'll always know what you'll have to pay ... any conservator who does not quote an exact rate is NOT on the up & up , as professionals go ... in case you're considering using one o' those .
Sometimes one can simply use a pallette knife & separate the photo from it's backing in a dry state (this really depends on many variables) & will work just fine , but that's not always !!!
You never know what might turn up , esp stamps/writing on the back of old photos , so care must be taken to watch for any signs of ink , while doing any wet separation processes !