As originally scripted, Luke did pull out his lightsaber.

So my guess is this got changed as they were filming it for out-of-universe reasons rather than in-universe ones. One reason might be framing around the Yoda puppet: in order to get Luke, R2, and Yoda in that image you posted, Luke has to be squatting. If he pulled out a sword from that position, it'd look ridiculous.

Another possible answer is they were concerned that the blue lightsaber effect would disappear into the blue background of Dagobah. This is famously why Luke's lightsaber color was changed to green in Return of the Jedi, so it could be visible in the outdoor shots aboard Jabba's skiff.

As originally scripted, Luke did pull out his lightsaber.

Nervously, he looks around at the foreboding jungle.

Luke: Still... there's something familiar about this place. I feel like... I don't know...

Strange Voice: Feel like what?

Luke jumps out of his skin. Artoo screeches in terror. The young warrior grabs for his lightsaber as he spins around, looking for the speaker. Mysteriously standing right in front of Luke is a strange, bluish creature, not more than two feet tall. The wizened little thing is dressed in rags. It motions toward Luke's sword.

Luke: (looking at the creature) Like we're being watched!

Creature: Away with your weapon! I mean you no harm.

So, my guess is this got changed as they were filming it for out-of-universe reasons rather than in-universe ones. One reason might be framing around the Yoda puppet: in order to get Luke, R2, and Yoda in that image you posted, Luke has to be squatting. If he pulled out a sword from that position, it'd look ridiculous.

Another possible answer is they were concerned that the blue lightsaber effect would disappear into the blue background of Dagobah. This is famously why Luke's lightsaber color was changed to green in Return of the Jedi, so it could be visible in the outdoor shots aboard Jabba's skiff.