Is there a way to change my character's appearance (hair, etc) safely without losing any abilities or skills? I tried using "showracemenu" but then I lost my racial frost resistance.

havent done it myself, but uesp says:

Note: Using this command has unwanted side-effects. When no modifications are made to the player model (no sliders adjusted) and the race is left unchanged, all active magical effects will be lost, including racial powers like the Nord's Resist Frost or the Altmer's Fortify Magicka abilities. To avoid the racial mod being lost, simply move one of the sliders to a new position and back, or switch from the race you were/are to a new race and then switch back while still in the race menu; all racial powers will remain, but any active buffs will get removed except for any standing stone abilities like 'The Lady' or 'The Warrior'. When race is changed, the player's skills will be changed to reflect the new race and its specific racial skill start modifiers. However, the majority of the skills will get reset to their starting values. The player's Health Magicka and Stamina will also unfortunately be set to 100/100/100 (best used at lvl 1). In addition, if the player is a werewolf and changes their race and then transforms into beast form, upon changing back their body will be changed back to whatever race they were when they were infected, with the head invisible. Your player character will lose racial abilities and some perks. Racial abilities lost in this manner will be automatically recovered the next time a game is loaded from the Main Menu (not quickload). If the perk Recovery was lost this way it will cease to function, even if it is removed and re-added.

Hope it makes sense.

I've used it with some frequency on a few toons - after adding hair/face/body mods for instance. The only thing I've found with it is that it sets the lip color back to the far left side of the slider on human/elf toons, and resets the fur color on Khajiit to grey/dark stripes - don't know about Argonian, I don't play them.

What I have NOT done is actually change race using it. That seems very iffy - and it's not something I'd do anyway. My girls are who they are from the word go.... I haven't had any issues with the racials getting wonky (but that may be due to not changing race?)

this will fix the loss of race abilities for you after using the showracemenu I use it after messing with my elfs appearance. if you change races it will jack all your stats up and there is no easy fix for that. You can only safetly use the showracemenu to change race at level 1 to reroll a new chacracter in riverwood.

http://www.uesp.net/wiki/Skyrim:Powers

So after using showracemenu to change appearance, just add the appropriate power back using the console?

I haven't had to do that at all. I would say - IF you are missing racials, then use that to fix it.