I'm creating a Svirfneblin Evil Mage by combining the stat blocks for each Evil Mage and Svirfneblin.
A Svirfneblin has the skills Investigation +3, Perception +2, Stealth +4. An Evil Mage has the skills Arcana +5, History +5 and saving throw proficiencies INT +5, WIS +3.
Does having 5 skills and 2 saving throw proficiencies cause major balance issues?
In my experience, skills like Investigation, Arcana, and History are rarely used by monsters. If you are in a game where they are used more often, this might have a bigger impact, but I doubt that having the skill proficiencies will affect balance significantly.
As for the saving throws, the Evil Mage already has these two proficiencies without much of an issue. That being said, if this homebrew character also has the chain mail that the typical svirfneblin monster stat block has, these proficiencies will strengthen its defenses against certain spells that the svirfneblin usually struggles with. I don't this is unbalancing, but it is worth considering.
To start with, CR is not always the best metric of balance; whether a changes to a creature is balanced entirely depends on what you are balancing against, and the other traits the monster has.
That being said, the Dungeon Master's Guide does provide guidance on how to calculate CR for monsters. This, while not a perfect metric for balance, is the best official guidance we have.
Saving Throw proficiencies are factored in to CR, skill proficiencies are not.
From the "Creating a Monster" section of Chapter 9 of the Dungeon Master's Guide:
If you want a monster to be unusually resistant to certain kinds of effects, you can give it a bonus to saving throws tied to a particular ability.
[...]
A monster with three or more saving throw bonuses has a significant defensive advantage, so its effective AC (not its actual AC) should be raised when determining its challenge rating.
Effective AC is used to calculate the Defensive Challenge Rating portion of a monsters Challenge Rating (which is averaged with the Offensive Challenge Rating), so having three or more saving throw proficiencies affects CR.
In your specific case of only two, it does not affect CR.
From the same section of the Dungeon Master's Guide:
If you want a monster to be proficient in a skill, you can give it a bonus equal to its proficiency bonus on ability checks related to that skill.
[...]
Skill bonuses have no bearing on a monster’s challenge rating.
The suggested way to add a race to NPC is to simply add the racial features from the NPC Stat Blocks section of the Dungeon Masters' Workshop in the DMG, as per the answer to How do you add a race to a race-optional monster?. Most cases don't include proficiencies, so this isn't an issue.
However, in this case, there are no additional skills and saving throws to be added, but ability modifiers are to be added.
The racial Ability modifiers for Svirfneblin are +1 Str, +2 Dex. This changes the Evil Mage's STR Mod to +0, and DEX Mod to +3. This changes the AC, attack bonus and damage bonuses and according to the DMG:
If the NPC’s AC, hit points, attack bonus, or damage changes, recalculate its challenge rating.
There should be no balance issues, but a new CR should be calculated using Creating Quick Monsters Stats Step 4.