Well, I won't discard the possibility of such a Hindenburg-Hammerstein Putsch too easily. ... also not the proposed time of 1932.
Hammerstein is known to have been ... 'sceptical' of Hitler since 1931 at least. Already in 1923 he titled him and his Putsch as "some private in Munich has gone mad" though such he might have said about every putschist at that time. IMHO it is rather fair to say Hammerstein was all these years 'aware' of Hitler and his and his party's development.
He was also kinda ... 'compagnion' - though probably too much of a word - or at least clollegial subordinate of Schleicher and his entourage around Hindenburg.
After the July election - as well as after the November election - of 1932 Hitler made himself with his continuing stubborn refusal of some kind of colation or 'shared' goverment 'impossible' to be trusted with power within said conservative militarian circles. ... including Schleicher, Bredow, etc. as well as Hammerstein.
With Papen also obviously 'failing' within the political sphere - like the frist session of the Reichstag after the July election sending him into dissolution of it without even having the chance to say a word at all before - Schleicher might come to the conclusion that the kind of coup d'etát as proposed in winter 1932/33 - and btw, by
some state lawyers 'approved' :
- declaration of National emergency well justfied by the daily political streetfighing and similar events
- dissolution of the actual goverment due to lack of support within the Reichstag followed by
- dissolution of the Reichstag at all
- adjourning by the 'power' of Article §48 and the State of Emergency any new election either repeatedly or for an undefined lapse of time "... until law and order are reestablished". ... with this definition left to the discretion of the Reichspresident ... and his entourage and govermental advisors.
In such a scenario Hammerstein might serve as the military 'face'. He later proved to be ready to participate in similar actions during Hitler reign on and again. Hindenburg would serve as the ... 'Ersatz-Kaiser and King" and offering a minimum of seemingly 'lawfullness'. Schleicher might act as the 'brain' behind' but he was never found of stanting in the spotlight.
Btw. ... also Hammerstein was noone keen on doing the nitty-bitty work of daily 'ruling'.
IMHO it would have to be someone else to take the part as 'face of the goverment' and the duties of the Reichschancellor.
Additionally maybe Schleicher might become convinced (by whatever minimalistic PoD you wish) sometime in Autumn 1932 that his IOTL preferred "Querfront"-concept of an alliance from the trade unions, conservative parts of the SPD over the civil service and the military to the Gregor Strasser wing of the NSDAP - won't work.
This might NOT be a 'democratic' Weimar but might evolve in time in kinda authoritarion pseudo-republik/democracy as there were so many in the first half of the 20th century.
... and a point to strat further discussions regarding the OP
P.S.: I recommend using the german wiki sources linked with some translator as first stops as they are much more detailed and rather well sourced that the anglophone wiki.
2.) No Hitler and no Nazis most likely means no WW2 as we know it.
IMHO matches it even better