Could I just wrap the exposed wire together and tape it tightly around with electrical tape if I do not wanna solder?
Yes, you can definitely do that. Just watch out because behind some receivers it will get hot and the adhesive on the electrical tape will melt off and then the tape will fall off. Also just taping the wires will not provide as secure or strong signal as a soldered connection. I have used just electrical tape for a once receiver before, but never again I did it once and it blew my radio fuse when the electrical tape fell off, two of the wires touched and shorted. I know people who have just used electrical tape and it worked fine for them but I would recommend soldering it so you won't have to do it twice if it comes undone and replace a fuse. Good Luck with the new receiver! If you have any other questions just let me know.
