Should I remove this mole on my penis? (Photo)

Holy Moley Ivan, you have a decision to make, so let's discuss the options.  
You could certainly leave the mole.  It's been there for years without causing an issue except the need to explain that it's only a mole that you have had for years and is not an STD......so your ego may get bruised sometimes...or you could remove it in one of several ways, but it will leave some kind of visible scar.
Option ONE: If you vaporize the pigmented part of the mole with a CO2 laser, down to normal tissue, and wipe away the char, you will still likely have a 5-6mm flat or slightly indented area of lighter tissue after it heals in for 4-6 weeks.  This is probably your best option as a light colored flat area is less troublesome that a dark mole that sticks up and has to be explained away.
Option TWO: Alternatively, because he skin is thin as you have noted, you could excise (Scalpel, CO2 laser or Radio Frequency Scalpel) a small ellipse of skin, perpendicular to the shaft of the penis, containing the mole.  It has to be 2-3x as wide as the mole is around, in order to be able to close the resulting opening in a straight line (that runs with the lines of tension around the penis), without causing the skin to pucker.  That linear scar, 2-3x longer than the diameter of the current mole, will likely be a bit thicker than the skin and/or may stretch out over time.  It could be lighter or darker, thus leaving a more visible scar than Option ONE.
Cost to do the procedure described above, under local anesthetic in the office, will be in the $150-$500 range depending on which way you go and take under an hour of your time either way.  
The CO2 laser ablation/vaporization is probably the least invasive and least expensive route to go! 
This is a much better choice than trying to freeze the mole off with liquid nitrogen BTW.  Sprayed liquid nitrogen tends to cause more loss of pigment and less dependable destruction of only the target, so you could essentially trade an elevated dark lesion for a flatter, white one and still not have the issue resolved in one visit!
PS.  Also please don't apply over-the-counter wart removing/dissolving agents to your mole!  They won't work in this case, but will cause scaring and discoloration of the surrounding tissue.  
No urgency or life changing decisions to worry about, so take your time to make your decision and don't loose any sleep over this otherwise benign issue!
Hope that helps.  Good Luck! 
Best, Z