First off, do not get frustrated. This is a tough matchup, yes, but you'll make it even worse if you don't react calmly to pikachu's annoying attack style. Against thunder jolt spam, cancel it with rapid jab. Honestly, the pika can't do much except approach. If you see him coming straight for you, you can actually do the rapid jab again and catch him in it, or else ftilt. Beware of shield grabs though, and IIRC you can mash B for a nade to stop the chain grab.
Pretty soon the pika will start QAC'ing into aerials and trying to leave you guessing. What you need to know is what he will attempt through the QAC. Oftentimes, he'll go for a fast-fall fair which can lag cancel and combo into a dsmash, or a utilt->uair->nair. Dair is also common as it can leave him pretty safe above you. Bair once in a while if he has his back to you. Nair is rare since that is usually saved for a KO move. Knowing an aerial is likely to follow, your best asset in this case is grenade countering. All of Pika's aerials force him to reach "into" the shield area, so to speak, and thus always hit the grenade. If you keep up the smart grenade countering, you will notice a decrease in the amount of QAC'ed aerials that the pika does, and often hesitation.
Speaking of dsmash, do not forget that if you're caught in that, always DI hard left or right (aiming away from the edge of the stage if possible). If you do not DI, you will get caught in thunder at a high altitude and likely die at a low percent (well , low for Snake, 80-90ish%). If you end up shielding it, make sure you spot dodge near the end of the dsmash or else it will poke through your shield.
When you're recovering, you can try a stalling tactic to avoid getting hit by thunder. As you're DI-ing your fall towards the stage, and you see Pika jump out for a thunder, DI backwards and make your falling path near vertical. As soon as thunder ends, up+B towards the stage and past pika.
As for edge-guarding, it's very difficult to do anything consistently effective against a smart pikachu. Ledge dropping grenades and mortar edge-guard don't do very well due to quick-attack ledge stall. They have a chance to hit, but the pika can just be very careful and ledgehop while DI-ing away and thunder jolting. If you get up close, make sure you have a grenade in hand and shield because the pika might ledgehop into an uair or fair. There is one trick that you can apply. If you spam mortars and force the pika to go below the stage, you can fast-fall edgehog (hugging is the correct term, I think) and make his up+b miss the edge at the last moment. It's a neat trick to be used once in a while, especially against those who recover from below.
If you get the Pikachu to realize you can't be camped with thunder jolts or pressured with QAC, you're slowly shifting the match in your favor. It's your turn to make your move. Mortar slide if he's holding back on thunder jolts. Start using grenades offensively and cooking them. Plant mines and c4 during his hesitation. Use your passive aggression (oxymoron, yes) to rack up damage. However, it's surprisingly tough to finish a pika off if he plays extremely defensive at high damage. Try to fool him with the range of utilt, and although it can be tough since QAC is tricky and lagless, use ftilt for a KO move as well. You may be able to bank on a mine to KO him if he's careless, though not many experienced Pikas are.