When the resistor is not loaded down, the voltages imposed upon the electrolytics will be excessive. Be sure that your present electrolytics are rated for at lest 400 WVDC. If not, replace with 400 or 450 WVDC electrolytics. Be sure that all other condensers within the set are rated for at least 400 WVDC.
Regarding fraying wires, the wires coming out of the transformer may be sleeved with heat shrink. Better yet, purchase some beautiful cloth covered hook-up wire in all of the colors available from www.tubesandmore.com. Then splice on the appropriate colors inside the transformer (end bells removed). Throw away the old wires. Be sure that you made a chart for the new wires, if any of them don't match the original color code. Place heat shrink over each wire and leave it long enough so that it goes all the way from where each wire enters the paper wrapping of the transformer, to the hole in the end bell where the wires pass through. Thread the wires through the bell and reassemble the transformer. Your transformer now has fresh wiring.
If any of the other wiring in the radio is in terrible shape, replace it, too, or cover bad spots with heat shrink tubing. If a wire is only stiff, leave it alone. It'll be fine sitting under the chassis where noone disturbs it. If a wire is in dangerous shape, attend to it!
There are in-rush current limiters available. My RCA color bar-dot-crosshatch generator came equipped with one in 1957 (it has a solid state rectifier). I do not see them as a necessity for most equipment with tube rectifiers, especially if the rectifier is filamentary. Filamentary rectifiers warm in a very uniform manner, and cool almost instantly when the switch is turned off. They afford much electrolytic protection, and they afford their own protection, because the cathode is almost never fully warmed when the electrolytics are first charging up (which makes for a lot of current that the rectifier must handle). Tubes which keep their cathodes hot for quite a while, like the 6X5, tend to flash over when the set is turned off warm and then back on right away. The electrolytic charge-up overloads the tube. Most of my AC radios (if not all) have filamentary rectifiers. I use them quite often and have no trouble with overloads or breakdown.
Thomas