Wouldn't the current want to flow through the wire rather than arc through the resister internally?
Current doesn't
want to do anything. It just is or it isn't, either case being determined by well-known laws of physics. All resistors have a voltage rating whose absolute maximum value is determined by the breakdown resistance of their surrounding environment, usually air, but sometimes a better insulating gas, such as nitrogen or sulfur hexafluoride, is used. It is common practice to connect equal-valued resistors in series strings to increase the breakdown voltage of the string. Below I discuss an example of this practice.
A small tandem particle accelerator I used to operate and maintain had several hundred ordinary two-watt carbon composition resistors soldered together in series and then spiral-wrapped around the accelerator columns. About every fifty resistors or so (I don't recall the exact number), the spiral string would connect to an accelerator plate on the column. There were some fifty or sixty of these plates, each with a central hole through which ions passed, stacked alternately with insulating glass rings in between, for each of two accelerator columns.
The entrance plate was at ground potential but the plate on the opposite end, through which accelerated ion particles emerged, could be as much as one million seven hundred thousand volts positive with respect to ground. The interior of the accelerator columns was maintained at a high vacuum, but the exterior was housed in a pressure vessel filled with dry SF
6 pressurized to 120 psig. Even so, there would be an occasional "tank arc," even when operating at less than maximum potential.
Tank arcs were infrequent, after proper "conditioning," but every once in awhile a cosmic ray would create an ionized conduction path and cause a tank arc to happen. I first witnessed this phenomenon in the 1950s at the Oak Ridge Atomic Energy Museum that I visited as a pre-teenager while living with my grandparents, who lived in Morristown, TN. One of the museum exhibits was a large tank with glass sides and metal plates for the top and bottom. The plates constituted a parallel-plate capacitor that was energized with several thousand volts DC. About once an hour or so, this capacitor would discharge with a loud crack (sounded sort of like an M80 firework) that could be heard throughout the museum when a cosmic ray passed through the tank. It is impossible to shield against cosmic rays, but the ones that reach the surface of the earth are infrequent over small areas. The museum tank was perhaps two square meters in area and was discharged by a cosmic ray no more often than once an hour.
So, to answer the question... go ahead and connect resistors in series to increase the voltage rating of the string. Common resistors have 1000 V DC or less ratings, so plan on using perhaps a dozen or so to safely reach 10 kV. Or look on eBay for "new old stock" high voltage resistors, sometimes available at reasonable prices. If making your own series strings (recommended), you are free to make up any resistance value you choose, a major advantage over purchasing ready-made high-voltage resistors which are generally available only in a limited range of values.
I suggest that you also slide a close-fitting length of thick-walled Tygon tubing over the resistor string to decrease the chances of arc-over across individual resistors. Seal the ends with clear RTV cement to keep moisture out and it should give you years of trouble-free service.
