35c might be a bit too wide for your rims, maybe 32c would be a better choice. They may fit your wheels just fine, but they may or may not rub on the chain stays, seat stays or the brake caliper.
35c tires are not only wider, but also have a larger outside diameter than than their smaller counterparts.
If you have enough clearance on your frame & calipers, you should still consider how big of a change in size you want to try.
Consult the chart below to help determine if they will fit.
From Tire Sizing Systems
Although you can use practically any tire/rim combination that shares
the same bead seat diameter, it is unwise to use widely disparate
If you use a very narrow tire on a wide rim, you risk pinch flats and
rim damage from road hazards.
If you use a very wide tire on a narrow rim, you risk sidewall or rim
failure. This combination causes very sloppy handling at low speeds.
Unfortunately, current mountain-bike fashion pushes the edge of this.
In the interest of weight saving, most current mountain bikes have
excessively narrow rims. Such narrow rims work very poorly with wide
tires, unless the tires are overinflated...but that defeats the
purpose of wide tires, and puts undue stress on the rim sidewalls.
Georg Boeger has kindly provided a chart showing recommended width
Which tire fits safely on which rim?
Note: This chart may err a bit
on the side of caution. Many cyclists exceed the recommended widths
with no problem