Most probably your gun was delivered from the factory as a Peruvian contract 1891 Argentine rifle (29+" barrel)

Later around 1912 and with the Peruvian 1909s already delivered, someone in the Peruvian Armed forces decided to "upgrade" the stocks of 1891s to the then-new Spitzer bullet, so a lot of replacement barrels were ordered to the Swiss SIG factory, both in rifle and short rifle configuration, and with the adequate contour to mount the "Lange-Vizier" or "Rollercoaster" sights; they show no other marking than "S.J.G." stamped close to the chamber area. Those are usually called "Modificado Peruano" (Peruvian modyfyed) or "Modelo 1912" (Model 1912) around here.

Some 1891 rifles were fitted with the new barrel, sights and handguard keeping the original configuration along with the stock; others were fitted with shorter barrels to give them a "Carbine style"; bolts were turned down and stocks cutted to fit the same barrel bands to the new barrel lenght. They, along with all the later short rifles or "Carbines" were known by local troops as "Mulitas" (Small mules) due to the sturdy recoil.

All this was made locally, and included polishing recievers and all the metal parts to eliminate original finish, rust, light scratches and pittings, thus erasing partially or completely some or all the stamps, including National crests, lettering, stamps and even serial numbers (Those were renumbered either with the original series or with a new, usually 4-digit number) according to the damage each rifle shown. Metal was then reblued and wood sanded or repaired if neccesary and then refinished; new handguards were also made. It's quite common to find them with no or partially scrubbed crest, although some keep all the factory markings.

No matching parts are virtually the rule in this gun since local armorers never took care about this. Yours is the "Carbine" model and any late-model (With the magazine catch screw) 1891 Argentine trigger guard and magazine assembly along with the rifle fronf and rear barrel bands would be a correct replacement. If you're looking for a stock, the "originals" are hard to come by, but any Argentine 1891 rifle stock would do AFTER you've altered to this particular configuration (Basically chopping the last 5" or so and refitting the front barrel band. You'll have to custom-make a wood hanguard by altering a Mauser Gew98 handguard to fit properly.

According to a few local old-timers these guns were kept in storage as reserve or assigned to horseback Police units, along with Navy and artillery troops; usually they are found with mint barrels, seldom if ever fired. Good luck with your gun....looks like a cool proyect.

Here's a link of how your complete gun should look:
http://www.carbinesforcollectors.com/perunavy.html