You will need a new flasher, or add load resistors to draw enough power to get the original flasher to work. A 2-terminal electronic one should work with 2 regular bulbs and 2 LED bulbs - like leave the fronts as is and put in LED rears - but will not work with all LED signals. A 3-terminal one will flash any LED setup, but most will flash really fast with just LED lamps, this is a safety feature and is supposed to tell you a signal bulb is burned out... low lamp current (like with LEDs) means a lamp is dead with normal lamps.
Right angle LED bulbs are available, but I haven't seen any good ones. The only acceptable brightness LED lamps I've found (I have a box of them, all dim, that cost a pile) have Luxeon 3 or 5 watt LEDs, and are frigging bright. I have one with about 15 "high intensity" LEDs that's useless, the "bulb" with one Luxeon is amazing.
If you're trying to save power a load resistor for the signals doesn't hurt much at all, unless you leave the signals on all the time.