The only plane mounted weapon that would cause noticeable recoil and a shudder would be on Guynemer's inspiration and modification plans for the Spad 7, which would be called the Spad 12. It carried a 37 mm cannon that fired through the prop shaft.
As a matter of fact quite a number of WW1 planes were equipped with cannons and sometimes very heavy ones, for instance the 57mm Davis Cannon.
The British RNAS used aircraft equipped with cannons of various types: 2-pounder (40-mm cal), 6-pounder (57-mm), 12-pounder (76-mm), and 50-pounder (127-mm). Thes guns had a muzzle-velocity of about 1200 ft/sec (370 m/sec) and an effective range of about 2000 yds (1846 m). The 2-pounder weighed 70 lbs (32 kg), the 6-pounder 208 lbs, and the 12-pounder 208 lbs, including mounting. Service installations of the 2 Pr Davis gun included a couple of D.H.4s at Dunkirk in 1917, and an R.E.8 in the Middle East in 1918 in which the gun was aimed forwards and downwards at a 45º angle for ground attack.
The RAF routinely used 1 pdr Vickers automatic cannon Mk III on the FE2b fighters of No 100 squadron in 1917 for train busting. It fired a very short 37 x 69R mm case (300 m/s) loaded in belts of 25.
in October 1918 a 1-and-a-half Pounder COW (Coventry Ordnance Works) gun was fitted in the rear cockpit of three D.H.4 light bombers, angled upwards at 45º for use against the giant R-plane bombers as well as Zeppelins. A hole was cut into the upper wing for the gun to fire through. Aiming was the job of the pilot, who instructed the gunner/loader when to fire. Various mounting, handling, sighting and buffer problems were resolved and over 1,000 rounds fired but the muzzle blast caused problems and the plane required light alloy plating to protect it, as well as some structural strengthening. In the event, just three D.H.4 aircraft fitted with this gun entered service in November, and only two of these reached the front, but they had no time to see action before the Armistice.
The French used a large range of cannons on their bombers. The first of the French 37 mm airborne cannon was the powerful M1902 "Tube Canon" which fired a 37x201R cartridge. The other common French aircraft weapon in this calibre was the short-barrelled naval Hotchkiss M1885, chambered for the low-velocity 37x94R cartridge. The M1885 was later modified with a smoothbore barrel to fire the "shotgun cartridge" shells in some fighters, as a rifled barrel disturbed the pattern of shot. Various sub-types of the Voisin aircraft were available with these cannon throughout the war, flexibly mounted in the front gun position of the pusher aircraft. The Breguet 5Ca2 was also originally fitted with a 37 mm cannon for bomber escort purposes, as was the Caudron R.14 which appeared too late to see action. Even larger guns were tried, including 47 mm Hotchkiss guns which were fitted to some of the last Voisins (for ground attack) and a Tellier flying boat (for anti-submarine use). Some success was achieved in shooting down balloons during the Verdun battle, and in March 1916 a Breguet 5Ca2 shot down an LVG with its cannon. The French even defined, in the spring of 1916, detailed specifications for cannon-carrying aircraft, designated Class D. The D1 types used the low-velocity M1885 37 mm gun and were intended for air combat, while the D2 models had the high-velocity M1902 version and were used for anti-balloon work and ground attack. Cannon-armed aircraft were never very common; by 1 February 1916 there were just twenty-five at the front, and only about sixty by August 1917. One of the last of the pusher planes, the Breguet 12Ca2 of 1917, was equipped with a searchlight as well as a 37 mm gun and stationed for defending Paris against Zeppelins.
The Germans used a 20mm Becker automatic canon on their two-seaters and heavy bombers, with great success. Such guns were mounted on the Friedrichshaven G.IIIa night bomber and the armoured AEG G.IVk bomber, and several Becker gun equipped G.IIIa, were delivered in September 1918, having a Becker in a nose mounting and using it to strafe ground targets when returning from bombing raids.
The first downward-firing installation was a rather makeshift effort in an Albatros J.I ground-attack plane, in which the Becker was fitted to the left-hand side of the aircraft, outside the observer's cockpit, allowing a limited range of movement. This was tested in the air in December 1917 and eight examples of this model were delivered to the Front for combat evaluation in the Spring of 1918. Other aircraft with downward-firing guns fitted in the observer's cockpit were the AEG J.II (twenty delivered in September 1918), and the LVG C.V (tested May-June 1918)
The Austro-Hungarians installed a 66 mm Skoda C95 L/18 Marine landing gun in the front cockpit of two large three-engined flying boats designated G3 and G6. It was used to fire at Italian naval craft (apparently without result) and thereby earned the distinction of being probably the largest-calibre weapon to be fired operationnally from an aircraft in the First World War.
The Italians produced one of the few fully-automatic cannon, the 25 mm Revelli-FIAT. This was flexibly mounted in the nose of a Macchi L flying boat, a dozen Savoia Pomilio S.P.2, and a similar number of Caproni bombers, mainly Ca.3 but also Ca.4 and Ca.5.
For more extensive details it's worth giving a look "The Flying Guns – World War 1: Development of Aircraft Guns, Ammunition and Installations 1914-32" by Anthony G Williams and Emmanuel Gustin.