No. You need new regulator, hose, and flash arrestors. Depedning on your torch, you may need different tips.
No, you do NOT need a new regulator or new flash arrestors or check valves (I'll explain the hose question below). Any acetylene regulator can be safely used with propane. If your regulator happens to have a POL CGA-510 fitting, it will work directly with a propane cylinder. If it is CGA-300 style regulator, you will need an adapter (usually you get adapters to go the other way though). If you have a CGA-200 (MC) or CGA-520 (B) regulator, do yourself a favor and get a real regulator. It is important to understand that the material components inside both acetylene and propane regulators are all the same, so propane will not damage an acetylene regulator and vice versa, even though regulators are sold specifically for these two gases.
As for other acetylene/propane gas cross compatibility issues, it's been covered here many times, but I'll rehash what you need to know.
Acetylene regulators have gauges that stop at 15 PSI output. The regulator may go higher, but the gauge is just a red bar above 15, because that high pressure is unsafe with acetylene. Output pressures above 15 PSI are perfectly safe with propane, so a dedicated propane regulator will have a gage that goes to 30 PSI (or more), but outside of some gigantic heating tips you simply will not have need for so much pressure. You certainly do not need that much pressure for cutting or brazing.
Check valves and flash arrestors will all be cross compatible with most fuel gases. Hydrogen MAY be the only exception, just because ordinary sintered metal flashback arrestors are insufficient to stop a flashback with hydrogen so people usually resort to bubblers, but even then, it isn't as if hydrogen will damage these components, so if you have a torch with them integrated (which I'd usually recommend) feel free to use it with any fuel gases you want.
Regarding hoses. Grade "T" hoses are compatible with ALL fuel gases. Acetylene, propane, you name it. Grades R and RM are ONLY compatible with acetylene (R is plain rubber, and RM has an oil resistant outer layer, but the interior is still rubber). Other fuels will degrade the rubber found in grades R and RM hoses, and because the issue starts on the inside, you will not have any visible signs of a problem until the hose fails.
Acetylene cutting and heating tips have a flat front surface with holes for the mixed gases piercing it. Propane cutting and heating tips have this pierced surface recessed a little. You can convert acetylene cutting or heating tips to work with propane by pressing on a ring cut from copper pipe* to protect the base of the flames. Or you can just buy propane cutting or heating tips. Single hole brazing tips are compatible with both types of gases.
*Pure copper is dangerous around acetylene, so don't use your converted tips again with acetylene unless you remove the copper.
One thing you WILL need new are shades. Oxy-acetylene flames are very bright, and you need a shade 5 lens when working with O/A to protect your eyes from their white light. Oxy-propane burns much cleaner, and you will quickly discover that it is impossible to spot the central cone of an oxy-propane flame through shade 5 lenses, so you will want something close to shade 2 (dark sunglasses) to be able to adjust yourself to a neutral flame. Also, oxy-propane does not produce a "feather", so expect the flame to look weird until you get used to it. The problem here though is sodium flare. That bright orange flare you get off of flux while brazing may be too bright for shade 2 lenses, and that's why I gave up on trying to use oxy-propane with brazing (it is fine for flux-less silfos brazing and cutting though).